{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 电导率测量误差分析\n",
    "--------------\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "sp.init_printing()\n",
    "%matplotlib inline\n",
    "#plt.rc('font', family='SimHei')\n",
    "\n",
    "def equation(fName, x):\n",
    "    fy = sp.Function(fName)\n",
    "    return sp.Eq(fy, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 概念\n",
    "\n",
    "电导率（conductivity）是用来描述物质中电荷流动难易程度的参数，通常用 $ K $ 来表示，单位是 $ 西门子/米 $，简写做 $ S/m $。\n",
    "\n",
    "### 测量原理\n",
    "\n",
    "电导率的测量原理是将相互平行且距离固定为 $ L $、面积为 $ A $ 的两块极板（或圆柱电极），放到被测溶液中，在极板的两端加上一定的电势（为了避免溶液电解及产生极化效应，通常为正弦波电压，频率1～3 kHz）。然后测量极板间电导 $ G $，则溶液的电导率 $ K $ 可表示为：\n",
    "\n",
    "$$ K = \\frac{LG}{A} $$\n",
    "\n",
    "其中$ G $ 为板间电阻 $ R $ 的倒数，即 $$ G = \\frac{1}{R} $$ \n",
    "\n",
    "设电极为圆形，其直径为 $ D $，则根据圆周面积公式 $ A = \\pi (\\frac{D}{2})^2 $ 有：\n",
    "\n",
    "$$ K = \\frac{4 L}{\\pi D^{2} R} \\tag{1} $$  \n",
    "\n",
    "从上式可知，确定电极的参数后，只需测量电极间的交流阻抗即可计算出溶液的电导率。交流阻抗测量使用下图所示的555定时器电路间接测量\n",
    "![555定时器测量电阻](https://gitee.com/ufbycd/ipynb/raw/master/555.gif \"555定时器测量电阻\")\n",
    "\n",
    "图中 $ R_2 $ 两端即为两电极，其阻值即为电极间的电阻 $ R $，根据555定时器的振荡规律可得:\n",
    "\n",
    "$$ R = R_2 = (\\frac{1.44}{F C} - R_1) \\div 2$$ \n",
    "\n",
    "化简可得：\n",
    "\n",
    "$$ R = - \\frac{R_{1}}{2} + \\frac{0.72}{C F}  \\tag{2} $$\n",
    "\n",
    "* 其中 $ F $ 为测得的定时振荡频率，$ R_1$、$ C $ 均已知。\n",
    "\n",
    "综上所述，联合公式 $ (1) $ $ (2) $，主要测量出555定时器的振荡频率即可计算出溶液的电导率：\n",
    "\n",
    "$$ K = \\frac{4 L}{\\pi D^{2} \\left(- \\frac{R_{1}}{2} + \\frac{0.72}{C F}\\right)} \\tag{3} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## 误差分析\n",
    "\n",
    "设间接测得量 $ N = f(x_1, x_2, x_3) $，其中 $ x_1，x_2，x_3 $ 均为彼此相互独立的直接测得量，每一直接测得量为等精度多次测量，它们的绝对误差分别为 $ \\Delta x_1，\\Delta x_2，\\Delta x_3 $ 那么 $ N $ 的绝对值传递规律为：\n",
    "\n",
    "$$ \\Delta_N = \\left|\\frac { \\partial f }{ \\partial x_1} \\right| \\Delta_{x_1} + \\left|\\frac { \\partial f }{ \\partial x_2 } \\right| \\Delta_{x_2} +  \\left|\\frac { \\partial f }{ \\partial x_3} \\right| \\Delta_{x_3}$$\n",
    "\n",
    "### 电阻测量误差分析\n",
    "\n",
    "将电阻测量公式 $ (2) $ 套用误差传递规律分析，得电阻测量的误差传递公式为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide_input": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\Delta_{R} = 0.72 \\Delta_C \\left|{\\frac{1}{C^{2} F}}\\right| + 0.72 \\Delta_F \\left|{\\frac{1}{C F^{2}}}\\right| + \\frac{\\Delta_{R_1}}{2}$$"
      ],
      "text/plain": [
       "                         │ 1  │                 │ 1  │   \\Delta_{R_1}\n",
       "\\Delta_R = 0.72⋅\\Delta_C⋅│────│ + 0.72⋅\\Delta_F⋅│────│ + ────────────\n",
       "                         │ 2  │                 │   2│        2      \n",
       "                         │C ⋅F│                 │C⋅F │               "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R,R1,F,C = sp.symbols('R,R_1,F,C')\n",
    "dR,dR1,dF,dC = sp.symbols('\\Delta_R,\\Delta_{R_1},\\Delta_F,\\Delta_C')\n",
    "R = (1.44 / (F * C) - R1) / 2\n",
    "dR = sp.Abs(sp.diff(R, R1))*dR1 + sp.Abs(sp.diff(R, C))*dC + sp.Abs(sp.diff(R, F))*dF\n",
    "equation(\"\\Delta_R\", dR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中：\n",
    "* $ \\Delta_C $ 即电容器的精度等级可选 $ 2\\% $ 的，则其绝对误差为 $ \\Delta_C = 0.01C $\n",
    "* $ R_1 $ 电阻一般选择精度等级为$ 1\\% $ 的，则其绝对误差为 $ \\Delta{R_1} = 0.01R_1 $\n",
    "* $ F $ 是微控制器对脉冲信号的计数值，其内部计数频率分频于晶体振荡器，其精度一般由基准精度及温漂特性决定，一般可满足 $ 200 ppm $ 相对误差等级，则其绝对误差为 $ \\Delta_F = F \\times 200ppm = F \\times \\frac{200}{1000000} = 0.0002F $ \n",
    "\n",
    "计算并画出电阻测量误差的分布图如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vrogzPpVgbMLfOyBXrlzp6/YLpTnt0px2aU7v5TuS+DrwR8BncaYQXQrcIyJi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1872bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 0.047*1e-6\n",
    "dc = 0.01 * c\n",
    "r1 = 1000\n",
    "dr1 = 0.01 * r1\n",
    "_rs = []\n",
    "_drs = []\n",
    "for f in range(200, 10000, 100):\n",
    "    dct = {C:c, dC:dc, R1:r1, dR1:dr1, F:f, dF:0.0002*f}\n",
    "    r = R.subs(dct)\n",
    "    _dr = 100 * dR.subs(dct) / r\n",
    "    _rs.append(r)\n",
    "    _drs.append(_dr)\n",
    "    \n",
    "_, ax = plt.subplots(1,1,sharex=True)\n",
    "ax.plot(_rs, _drs)\n",
    "ax.set_title('电阻测量误差分布',fontsize=15)\n",
    "ax.set_xlabel('$ R (\\Omega) $',fontsize=15)\n",
    "ax.set_ylabel(\"$\\% $\",fontsize=15)\n",
    "ax.set_xlim(0)\n",
    "ax.grid(linestyle='--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由公式 $ (3) $ 及电阻测量误差分布图可知：\n",
    "* 误差的走势规律基本就是按 $ \\frac{1}{C} $ 的变化规律，电路设计时应该合理设计电极参数尽量使用其电阻值落在大于 $ 500 \\Omega $ 的区间；\n",
    "* 电阻测量的误差绝大部分来源于电容 $ C $ 的误差，应尽量使用高精度的电容器；\n",
    "\n",
    "### 电导率误差分析\n",
    "\n",
    "将电导率公式 $ (1) $ 代入误差传递规律分析，得电导率的误差传递公式为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAAhCAYAAAD6QI3vAAAABHNCSVQICAgIfAhkiAAACj9JREFU\neJztnXuMHVUdxz8L1ALWlodYiIHeFkEqaNoukli0rEoQAulDC1Vjw1ZFMRGtoKVisAcSbSuGgI1P\nMLjURi1IVaryqFq1oBjBtoDIogimMaDWWkQqZen6x++Md/bsmbnznrnb3ye5uXvPnDnnd+Z7zpzX\nb2ZBURRFUZT9jl8AN9dthFI6c4Dbgb8Cw8DCes1RamBMtPUD6jZA6UgPMAO4v25DlNJ5KbAN+HDd\nhii1oG1dqYwTkdHrG+s2RKkUnbHsf4yZtq4zlmowSIVpZTi3F9gHbC3QHshnk+LH0LxramieTWMF\nQ7HXtqy2HsZQQX2I61g+ZQ0YBl5dphEFcy5wF7AD2AM8DtwCvKHDeU0t7yxgEHi2hrwnAy8CX6gh\n76wspq3j+xPEb6ruVaI6N4M623qY3PUhqmPpAd4H7La/L8qaQcWsBjYiAt0BXA88AMwD7gHeE3Fe\nk8vbS31rrvOQOrKhpvzTciywhuQNs8m6V4nq3AzqbOthcteHqI7lLGAqcmN+ELgQeEnWTCriaODj\nwNPAa5BRzHJknfptSOW6OuLcJpd3JvVVtgXATsRTpSz6kVFkX850eoCbEHu/kvCcJuteJVXoDMVo\nPZZ1rrOth8ldH6I6lqBHvxkYAF5uM2syU5Dy3Af8zTn2M+DfwFER5za1vNOAw5BZV9VMAt6CuL++\niCwxDif8zKjB3o9Ye5cA/0l4TlN1rxJXZ2i21mNV5zrbephC2r2vY5kMzAV+CfwJWGcz+EA55SiM\nx4C9wGlIxQkzB3gZsMlzXpPL22u/XwBOCX2mV5D3ucio7jb7ezfwZfv3w8BVoc93bPgWYAWwvQL7\nwkwHViEj0qSjrCbqPgFpnEEDbdm/jysxT1dnaK7WY0VnH3W29TCFtPuDPAkvAcYhPTvAU8hm+NnA\nq4A/FlSApUgPnZStwPdijv8TuBy4Fvi9jbsTOB6pWHcDH/ScV1V5szDLft/jhD8EvLbkvBcgI8K7\n7e8tyIzvQ8i1NaG4y4BFwDeAr5dsl8tBwFrgL8AVKc5rou6nIrPrgGvs9wCyjFQGrs7QTK3Hks4+\n6mzrYUpp9z3IhX4OmBgKX4RMdVblNrvNEySfYg1b45MwH+lkwuc+BrzbE7eq8hqa5/JpiLbpYGTp\n8BYn/Cr8z1d824b3kp5+8q27X42MQMNef4Z4b6GydA/ybWU8vwwM6XWG5mndJJ3d/Fs506kSQw3t\n/q024jpPhruQ3n6cc+ynnvgXIWIu75RhwSwDhpBZyzTgUGQkcCdSrs858bOUF6TMQac1hDgM3I6s\nTfowNK8CGqJtmmuPuZ3x9234CU74IDKFH98hzycodjBxGnL9XV0N8TecrLp3et1GkG8rJk7VGNLr\nDM3Sumqdw+37BaTM7/XEC/JvxdjeNAwVtHt3KSxYdxxwwv8LrLfH5wG3ho7NRFx8sRl8EZk1zGPk\n9Lps+hB34w3ApaHwB5Dp3SBwGeJJ8rg9lqW8IGVeAXwNqaTH2bibgHfRXnvsVhYg+1U/dMJnIC6e\n4eWDCciSwsPA8x3SvY7Ry58zkGs8gNyMwsQ9KBYsjQwCV3bI1yWL7sHrNr6bMq8mE6UzNEfrqnUG\nad9XIN5n45El9BuB31L9/mGVlNLuj7IRduDf1J+N9Fp3hcKOt2FnIL7lv0Fu5K0EhViK9J5JP/M7\npPd5a8slEcdvs8ffYX9nKS+0y9znOWcj7U4rjGHkKCHNSK7IT5xNAQcC/wB+7IQfbuO7a8BvsuFr\nPeVOQj/ZlkcOI3m5rwudl1X3JK/bMIy+pnVr7bMJonWGZmldtc5B+54ZCmvZsHc6cQ3N0btR7T48\nY7kQ8QZYi7xWwOVeZK/iTMQn/M/I2towcATS6/8IuBh54r0TSxEX4aQMEL95H0zHolyKg/C99jtL\neaFd5t95zrkT8aqYCDwTY2tPzLG6mQMcyeiHowJPpW1OeLDpWOZrKHw8T/SG4SzkxrAFeBT4VehY\nHt2zvG6jqVpH6QzN0roOnZ+hPTM5BlmC24e/zbs0Ve9OlNbu/4DcME+KiXOljfMZ+3s1svY5hDyc\nWCcXILY9BbzSOXYOUjH2IBcPspUXpMyDEfEvtvEPccIN/lFCGu5FxH0I+HSOdAIMfpvWIJukk53w\nj9n4rpvmDTb8rIx29JNtxhKHsWn61t6z6n4N8EjCfFvJzBzFscBmxKtxG/D2jOkksSlKZ+gerQ3F\n67wauS7PIvvEw0jn9tGY/FuprB5JEZqnScNQQbsPZix9yPtz9hDfQQSZLkH2GHqBnyDizYo6qSJu\nRfY4zkRuABuQTmY6cB4ykliOuCD3ka28Q0iZox5iOhF4kmQztrScjYykDkRGaD+gnJHjfKQTe9oJ\njxq5HGG/T0Yq9o4SbCqKPvLpXvZT0UPIDWwb8Aqb3x3IDa5oonSG7te6j3w634gMJCYCK5GB5PUl\n2VqE5kWkUUq7X0f6dbvgsf/LgNchbmomRUHKYByyxPZr5CY8hDyFv5GRPWvW8oKU+RMReT+JeKS5\nGPKPbAIOQSpO3ieeDaNter0Nu9QTfysyojnUCV+ErM0+R7ZZaz/VzVjy6L4LGb0lybeVz/z/s538\nD0ca0ukM3aO1oXiddyLLaAFTkGtxckz+rZzlCFOE5nFpGJrR7iOZao15s/09F7mR+1wXxwpBmV23\n4h7gS8iFPsZznsFfAdO6Ld+HdOCrPceSukjG2fRZGzY15rz9kWnIdTmjQzxD9I0mrdanIjNvd81e\ndS6PoH27qy/3I9fMxVCc3uDXPK3eUfUmzuZG1YeFiDFhl8JliCvf7FosKp+gzCchL708ATgf+Dnw\nd+D0iPMM/gq4C9kvOdoemwN8E9kPWhSR1kTESeAUT1qftGlNQSrLPmQ2mdSmR6h+E74bOB+5VrOJ\nf92GIfpGk0brI5HlBV87Up3LYyEyOnf3SFchezYuhmL0hmjN0+gdV2/ibG5UfViJvHvH5SZk+akR\nvV/BrGTkKGQn4omyAlnbjMIwWswsbssBlzNy+pnGRTLOJsVPWPfw50EnnsF/TdNoPR55EHOxJ67q\nXC7BfopL8KCluxxmyK83RGueRu+4epPEZqULMYwW8wJk5DHJE/8SGz94DcUk2u7SByMOE+c5ae1G\nNvZBluPWI6OvqH9q5LNJyYfBf02Tat0DfIvovUrVuVkY8ukN8Zon1btTvUlic6H4XkKpFM9m+/2v\nUFgv8iTr7lGxZS01/H048sT3OORhr/W033YQpDXBpnUAMpXfi2zGPZrCJiUfm+23e02Tan06skyy\nnfYDwYtpz4xU52ax2X5n1RviNU+qd6d6k8RmZYywCXmJm49rGf3Ki05pfRV5xULwbrQ1eYxTCqUo\nrVXn7kD1Vmoji9tyXFpJXSSV6ilKa9W5O1C9lVrI6rYcl1ZSF0mlWorSWnXuDlRvpTayui1HpZXG\nRVKplqK0Vp27A9VbqY2sbstRaaVxkVSqpSitVefuQPVWFEVRFEVRFEVRFEVRFEVRFEVRMvE/InIb\nPIINPjAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\Delta_{K} = \\frac{8 \\Delta_D}{\\pi} \\left|{\\frac{L}{D^{3} R}}\\right| + \\frac{4 \\Delta_L}{\\pi} \\left|{\\frac{1}{D^{2} R}}\\right| + \\frac{4 \\Delta_R}{\\pi} \\left|{\\frac{L}{D^{2} R^{2}}}\\right|$$"
      ],
      "text/plain": [
       "                      │ L  │              │ 1  │              │  L  │\n",
       "           8⋅\\Delta_D⋅│────│   4⋅\\Delta_L⋅│────│   4⋅\\Delta_R⋅│─────│\n",
       "                      │ 3  │              │ 2  │              │ 2  2│\n",
       "                      │D ⋅R│              │D ⋅R│              │D ⋅R │\n",
       "\\Delta_K = ───────────────── + ───────────────── + ──────────────────\n",
       "                   π                   π                   π         "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K,_R,L,D = sp.symbols('K,R,L,D')\n",
    "dK,_dR,dL,dD = sp.symbols('\\Delta_K,\\Delta_R,\\Delta_L,\\Delta_D')\n",
    "K = L / (sp.pi * ((D/2) ** 2) * _R)\n",
    "dK = sp.Abs(sp.diff(K, L))*dL + sp.Abs(sp.diff(K, D))*dD + sp.Abs(sp.diff(K, _R))*_dR\n",
    "equation(\"\\Delta_K\", dK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "按当前设计的电极尺寸、精密级的加工公差来分析，其中：\n",
    "* 电极距离： $ L = 2.79 \\pm 0.01  (cm) $\n",
    "* 电极直径： $ D = 0.40 \\pm 0.005 (cm) $\n",
    "* 电阻值及其误差取电阻测量误差分析时算出的值\n",
    "\n",
    "计算并画出电导率测量误差分布图如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WVgbAxIkTqauro7i4GIDhw4czduxYli1bBkBcXByZmZksX768pRotKyuLoqIiysvLAUhN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1872b160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 2.79e-2\n",
    "dl =0.01e-2\n",
    "d = 0.40e-2\n",
    "dd = 0.005e-2\n",
    "_ks = []\n",
    "_dks = []\n",
    "for r, dr in zip (_rs, _drs):\n",
    "    dct = {L:l, dL:dl, D:d, dD:dd, _R:r, _dR:dr*r/100}\n",
    "    k = K.subs(dct)\n",
    "    dk = 100 * dK.subs(dct) / k\n",
    "    _ks.append(k * 1e4)\n",
    "    _dks.append(dk)\n",
    "\n",
    "_, ax = plt.subplots(1,1,sharex=True)\n",
    "ax.plot(_ks, _dks)\n",
    "ax.set_title('电导率测量误差分布',fontsize=15)\n",
    "ax.set_xlabel('$ K \\quad (\\mu S/cm) $',fontsize=15)\n",
    "ax.set_ylabel(\"$ error \\quad (\\%) $\",fontsize=15)\n",
    "ax.set_xlim(0)\n",
    "ax.grid(linestyle='--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 合并分析\n",
    "\n",
    "总的电导率公式为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL4AAAAkCAYAAAA3iYC4AAAABHNCSVQICAgIfAhkiAAAB1FJREFU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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$K = \\frac{4 L}{\\pi D^{2} \\left(- \\frac{R_{1}}{2} + \\frac{0.72}{C F}\\right)}$$"
      ],
      "text/plain": [
       "           4⋅L        \n",
       "K = ──────────────────\n",
       "       2 ⎛  R₁   0.72⎞\n",
       "    π⋅D ⋅⎜- ── + ────⎟\n",
       "         ⎝  2    C⋅F ⎠"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fK = K.subs(_R, R)\n",
    "equation(\"K\", fK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "总的误差传递公式为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hide_input": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x6xxvuwXiOprxAaTNbOQDTBeLsFFcG3rhy4D/CMQfUP4lYlPP29Ko0WeNTsTz9FLg54Hw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\nAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\Delta_{K} = \\frac{2.88 \\Delta_C}{\\pi} \\left|{\\frac{L}{C^{2} D^{2} F \\left(\\frac{R_{1}}{2} - \\frac{0.72}{C F}\\right)^{2}}}\\right| + \\frac{8 \\Delta_D}{\\pi} \\left|{\\frac{L}{D^{3} \\left(\\frac{R_{1}}{2} - \\frac{0.72}{C F}\\right)}}\\right| + \\frac{2.88 \\Delta_F}{\\pi} \\left|{\\frac{L}{C D^{2} F^{2} \\left(\\frac{R_{1}}{2} - \\frac{0.72}{C F}\\right)^{2}}}\\right| + \\frac{4 \\Delta_L}{\\pi} \\left|{\\frac{1}{D^{2} \\left(\\frac{R_{1}}{2} - \\frac{0.72}{C F}\\right)}}\\right| + \\frac{2 \\Delta_{R_1}}{\\pi} \\left|{\\frac{L}{D^{2} \\left(\\frac{R_{1}}{2} - \\frac{0.72}{C F}\\right)^{2}}}\\right|$$"
      ],
      "text/plain": [
       "                         │         L          │                               \n",
       "           2.88⋅\\Delta_C⋅│────────────────────│              │      L       │ \n",
       "                         │                   2│   8⋅\\Delta_D⋅│──────────────│ \n",
       "                         │ 2  2   ⎛R₁   0.72⎞ │              │ 3 ⎛R₁   0.72⎞│ \n",
       "                         │C ⋅D ⋅F⋅⎜── - ────⎟ │              │D ⋅⎜── - ────⎟│ \n",
       "                         │        ⎝2    C⋅F ⎠ │              │   ⎝2    C⋅F ⎠│ \n",
       "\\Delta_K = ──────────────────────────────────── + ─────────────────────────── \n",
       "                            π                                  π              \n",
       "\n",
       "                │         L          │                                        \n",
       "  2.88⋅\\Delta_F⋅│────────────────────│              │      1       │   2⋅\\Delt\n",
       "                │                   2│   4⋅\\Delta_L⋅│──────────────│          \n",
       "                │   2  2 ⎛R₁   0.72⎞ │              │ 2 ⎛R₁   0.72⎞│          \n",
       "                │C⋅D ⋅F ⋅⎜── - ────⎟ │              │D ⋅⎜── - ────⎟│          \n",
       "                │        ⎝2    C⋅F ⎠ │              │   ⎝2    C⋅F ⎠│          \n",
       "+ ──────────────────────────────────── + ─────────────────────────── + ───────\n",
       "                   π                                  π                       \n",
       "\n",
       "        │       L       │\n",
       "a_{R_1}⋅│───────────────│\n",
       "        │              2│\n",
       "        │ 2 ⎛R₁   0.72⎞ │\n",
       "        │D ⋅⎜── - ────⎟ │\n",
       "        │   ⎝2    C⋅F ⎠ │\n",
       "─────────────────────────\n",
       "        π                "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfK = sp.Abs(sp.diff(fK, L))*dL + sp.Abs(sp.diff(fK, D))*dD + sp.Abs(sp.diff(fK, R1))*dR1 + sp.Abs(sp.diff(fK, C))*dC + sp.Abs(sp.diff(fK, F))*dF\n",
    "equation(\"\\Delta_K\", dfK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中：\n",
    "* 电极距离： $ L = 2.79 \\pm 0.01 (cm) $\n",
    "* 电极直径： $ D = 0.40 \\pm 0.005 (cm) $\n",
    "* 基准电阻： $ R_1 = 1000 \\, (\\Omega) $ ，相对偏差 $ 1 \\% $\n",
    "* 电容： $ C = 0.047 \\, (\\nu F) $ ，相对偏差 $ 1 \\% $\n",
    "* 测得的频率 $ F $ 范围通常为 $ [200, 10000] \\, (Hz) $，相对偏差 $ 0.02 \\% $\n",
    "\n",
    "为了便于对比分析，依次计算并画出各物理量所贡献的误差及总误差，来对比分析各物理量对误差的影响程度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide_input": false
   },
   "outputs": [],
   "source": [
    "def be(s):\n",
    "    e = 0\n",
    "    if s < 6e-3:\n",
    "        e = 0.05e-3\n",
    "    elif s < 30e-3:\n",
    "        e = 0.1e-3\n",
    "    elif s < 120e-3:\n",
    "        e = 0.15e-3\n",
    "    elif s < 400e-3:\n",
    "        e = 0.2e-3\n",
    "    elif s < 1000e-3:\n",
    "        e = 0.3e-3\n",
    "    else:\n",
    "        e = 0.5e-3\n",
    "    return e\n",
    "\n",
    "def gdct(dl=0, dd=0, ddc=0, ddr1=0, ddf=0):\n",
    "    return {L:l, dL:dl, D:d, dD:dd, C:c, dC:ddc*c, R1:r1, dR1:ddr1*r1, 'ddf':ddf}\n",
    "\n",
    "def errors(l, d, c, r1, fMax):\n",
    "    dcts = {'All':gdct(dl=be(l), dd=be(d), ddc=0.01, ddr1=0.01, ddf=0.0002),\n",
    "            '$ \\Delta_L $':gdct(dl=be(l)), \n",
    "            '$ \\Delta_D $':gdct(dd=be(d)), \n",
    "            '$ \\Delta_C $':gdct(ddc=0.01), \n",
    "            '$ \\Delta_{R_1} $':gdct(ddr1=0.01),\n",
    "            '$ \\Delta_F $':gdct(ddf=0.0002)}\n",
    "\n",
    "    fig, ax = plt.subplots(1,1,sharex=True)\n",
    "    fig.set_size_inches((10,10))\n",
    "    for s, dct in dcts.items():\n",
    "        _ks = []\n",
    "        _dks = []\n",
    "        for f in np.linspace(1, fMax, 10):\n",
    "            dct[F] = f\n",
    "            dct[dF] = dct['ddf'] * f\n",
    "            k = fK.subs(dct)\n",
    "            dk = 100 * dfK.subs(dct) / k\n",
    "            _ks.append(k * 1e4)\n",
    "            _dks.append(dk)\n",
    "        ax.plot(_ks, _dks, label=s)\n",
    "    ax.set_title('电导率测量误差分布',fontsize=15)\n",
    "    ax.set_xlabel('$\\mu S/cm$',fontsize=15)\n",
    "    ax.set_ylabel(\"$\\%$\",fontsize=15)\n",
    "    ax.set_xlim(0)\n",
    "    ax.legend(loc='best', fontsize='x-large')\n",
    "    ax.grid(linestyle='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KgfRNCG8mzEoOZiVHKWb1xLcO4fDPrxb9cxfNrMFfPrB4zK/bsWMHurq6sHr1apw+fRob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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1acadf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 2.79e-2\n",
    "d = 0.40e-2\n",
    "c = 0.047e-6\n",
    "r1 = 1000\n",
    "errors(l, d, c, r1, 5600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由上图可知：\n",
    "* $D$ 跟 $L$ 确实是电极的固有属性，其对误差的影响不随电导率的大小变化而改变\n",
    "* $C$ 跟 $R_1$ 对误差影响随电导率变大而变大\n",
    "* 电极的加工公差对误差影响较大，应该选用较大尺寸的电极以减弱对误差的影响\n",
    "* 电容器的精度对误差的影响最为明显\n",
    "\n",
    "## 最优的管径和电极大小搭配\n",
    "\n",
    "从目前来看电极的加工公差对测量误差影响巨大，有必要用理论分析法而非拍脑袋法来确定电极参数；\n",
    "最优的管径（$L$）和电极大小应该使最终结果满足：\n",
    "* 测量范围尽可能落在应用的范围之内，不太大也不太小，即要求灵敏度不太大也不太小；其实就是要求在满足测量范围的前提下稳定度尽可能好；\n",
    "* 在测量范围内的测量误差尽可能小；\n",
    "\n",
    "### 电导率的灵敏度变化规律\n",
    "\n",
    "频率$F$与电导率$K$的关系由公式$(4)$变换可得："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJEAAAAoCAYAAAD+HRieAAAABHNCSVQICAgIfAhkiAAABtBJREFU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\n",
      "text/latex": [
       "$$F = \\frac{1.44 \\pi D^{2} K}{C \\left(\\pi D^{2} K R_{1} + 8 L\\right)}$$"
      ],
      "text/plain": [
       "                2      \n",
       "        1.44⋅π⋅D ⋅K    \n",
       "F = ───────────────────\n",
       "      ⎛   2           ⎞\n",
       "    C⋅⎝π⋅D ⋅K⋅R₁ + 8⋅L⎠"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K2,F2,dF2,ddF2 = sp.symbols(\"K,F,F',F''\")\n",
    "F2 = 1.44 * sp.pi * D**2 * K2/(C *(sp.pi * D**2 * K2 * R1 + 8 * L))\n",
    "equation(\"F\", F2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将$F$对$K$求导数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATsAAAAqCAYAAADMIfxNAAAABHNCSVQICAgIfAhkiAAACcpJREFU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\nsK8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\operatorname{F'} = - \\frac{1.44 \\pi^{2} D^{4} K R_{1}}{C \\left(\\pi D^{2} K R_{1} + 8 L\\right)^{2}} + \\frac{1.44 \\pi D^{2}}{C \\left(\\pi D^{2} K R_{1} + 8 L\\right)}$$"
      ],
      "text/plain": [
       "               2  4                        2     \n",
       "         1.44⋅π ⋅D ⋅K⋅R₁           1.44⋅π⋅D      \n",
       "F' = - ──────────────────── + ───────────────────\n",
       "                          2     ⎛   2           ⎞\n",
       "         ⎛   2           ⎞    C⋅⎝π⋅D ⋅K⋅R₁ + 8⋅L⎠\n",
       "       C⋅⎝π⋅D ⋅K⋅R₁ + 8⋅L⎠                       "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dF2 = sp.diff(F2, K2)\n",
    "equation(\"F'\", dF2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导数$ F' $的表达式较为复杂，不能简单地判断出其单调性；则$F'$对$K$对导数$F''$并解方程 $ F'' = 0 $ 通过观察方程的根来判断$F'$变化趋势："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVUAAAAWCAYAAABwtw9YAAAABHNCSVQICAgIfAhkiAAABm5JREFU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\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ \\left \\{ D : 0.0\\right \\}, \\quad \\left \\{ L : 0.0\\right \\}, \\quad \\left \\{ R_{1} : 0.0\\right \\}\\right ]$$"
      ],
      "text/plain": [
       "[{D: 0.0}, {L: 0.0}, {R₁: 0.0}]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ddF2 = sp.diff(dF2, K2)\n",
    "sp.solve(sp.Eq(ddF2, 0), C, D, R1, L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由方程的根可知，只能 $D = 0$ 或 $L = 0$ 或 $R_1 = 0$ 时$F'$的单调特性才有可能会发生变化，而实际中这些值都不会为$0$，故$F'$为单调变化曲线。\n",
    "\n",
    "求出$F$的灵敏度在$K$在$\\left [ 0, \\, \\infty \\right ]$内的范围为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAYCAYAAACIqH2FAAAABHNCSVQICAgIfAhkiAAABm5JREFU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\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ \\frac{0.18 \\pi D^{2}}{C L}, \\quad 0\\right ]$$"
      ],
      "text/plain": [
       "⎡        2   ⎤\n",
       "⎢0.18⋅π⋅D    ⎥\n",
       "⎢─────────, 0⎥\n",
       "⎣   C⋅L      ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[sp.limit(dF2, K2, 0), sp.limit(dF2, K2, sp.oo)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可知，频率 $F$ 的灵敏度随电导率 $K$ 的增大而减小，最小会变成 $0$；极限最大灵敏度只受限于 $D$ 、$L$ 跟 $C$ 的取值。\n",
    "\n",
    "### 最优化算法 \n",
    "\n",
    "电极参数的不同会直接影响电导率测量的误差、灵敏度、电路合理性等，而这此因素是相互制约此消彼长的。为寻找最优的电极参数，下面使用最优化算法来综合各因素以确定最优解。求解的原理很简单：算出所有可能的输入条件下的结果，从中找出最好的结果，该结果所对应的输入条件即为最优条件。\n",
    "\n",
    "输入条件如下：\n",
    "* 电导率测量范围至少满足：$\\left [ 300, \\, 10000 \\right ] \\, (\\mu S/cm) $\n",
    "* 管径 $L$ 取值范围： $\\left [ 1, \\, 6 \\right ] \\, (cm) $\n",
    "* 电极直径 $D$ 取值范围： $\\left [ 0.5, \\, 6 \\right ] \\, (cm) $\n",
    "* $R_1$ 电阻的取值会影响电路输出信号的频率跟和占空比，取值范围：$\\left [ 10, \\, 100 \\right ] \\, (\\Omega) $\n",
    "* $C$ 电容的取值会影响电路输出信号的频率，取值范围：$\\left [ 0.01, \\, 1 \\right ] \\, (\\mu F) $\n",
    "\n",
    "结果判断方法如下：\n",
    "* 电极两端电阻应大于$ 200 \\, \\Omega $\n",
    "* 电路的输出信号的频率应该大于$100 \\, Hz$且小于 $20 \\, kHz$\n",
    "* 信号的频率跟占空比不大于 $95\\%$\n",
    "* 电导率的灵敏度尽可能大\n",
    "* 电导率误差小于 $5\\%$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f555(r1, c, r):\n",
    "    return 1.44 / (( r1 + 2 * r) * c)\n",
    "\n",
    "def k2r(d, l, k, pi=np.pi):\n",
    "    return 4 * l / (pi * (d**2) * k)\n",
    "\n",
    "def duty(r1, r):\n",
    "    return (r1 + r) / (r1 + 2 * r)\n",
    "\n",
    "def pluse(r1, r, f):\n",
    "    return duty(r1, r) / f\n",
    "\n",
    "def maxDK(d, l, c, pi=np.pi):\n",
    "    return 0.18 * pi * d**2 / (c * l)\n",
    "    \n",
    "def errK(d, l, r1, c, f):\n",
    "    dct = {L:l, dL:0.01, D:d, dD:0.005, C:c, dC:0.02*c, R1:r1, dR1:0.01*r1, F:f, dF:0.0002*f, sp.pi: np.pi}\n",
    "    return dfK.subs(dct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vQ/N1qCXuA9AwrilmrrYXI0vMc4x5LmU6+A25DC3nHsPX563IcY/9Ijlb9Rfcbdew2uIy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\nmUwmk8lkMplMJpPJZDKZTCYzFP4f1ZCOzcMrL7AAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ C : 4.78947368421e-07, \\quad D : 0.0166326530612, \\quad L : 0.0436734693878, \\quad R_{1} : 100.0\\right \\}$$"
      ],
      "text/plain": [
       "{C: 4.78947368421e-07, D: 0.0166326530612, L: 0.0436734693878, R₁: 100.0}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ks = np.linspace(300e-4, 10000e-4, 10)\n",
    "ls = np.linspace(1e-2, 6e-2, 50)\n",
    "ds = np.linspace(0.5e-2, 2e-2, 50)\n",
    "r1s = np.linspace(10, 100, 20)\n",
    "cs = np.linspace(1e-8, 1e-6, 20)\n",
    "gdk = 0\n",
    "gek = 1\n",
    "best = {}\n",
    "for d in ds:\n",
    "    for l in ls:\n",
    "        for c in cs:\n",
    "            dk = maxDK(d, l, c)\n",
    "            for r1 in r1s:\n",
    "                pss = True\n",
    "                maxFK = {'f':1, 'k':1}\n",
    "                for k in ks:\n",
    "                    r = k2r(d, l, k)\n",
    "                    if r < 200:\n",
    "                        pss = False\n",
    "                        continue\n",
    "                    f = f555(r1, c, r)\n",
    "                    if f >= 20000 or f < 100:\n",
    "                        pss = False\n",
    "                        continue\n",
    "                    dt = duty(r1, r)\n",
    "                    if dt > 0.95:\n",
    "                        pss = False\n",
    "                        continue\n",
    "                    pl = pluse(r1, r, f)\n",
    "                    if pl < 1e-4:\n",
    "                        pss = False\n",
    "                        continue\n",
    "                    if f > maxFK['f']:\n",
    "                        maxFK['f'], maxFK['k'] = f, k\n",
    "                if not pss:\n",
    "                    continue\n",
    "                #ek = errK(d, l, r1, c, maxFK['f']) / maxFK['k']\n",
    "                #if ek > 0.05:\n",
    "                #    continue\n",
    "                if dk > gdk:\n",
    "                    gdk = dk\n",
    "                    best = {L: l, D:d, R1:r1, C:c}\n",
    "                    maxF = maxFK['f']\n",
    "best"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在此输入条件下的电导率的测量误差分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vrJdqUmlTx1TGnGRgTjKkek6P/fgADp7sTvr7Liz14PN3Lrqo127btg2nT5/GqlWr0NLS\ngqeeegrHjh3DvHnzprjKSyd+JC3VNgpMZdu3bzddAlnAnGRgTjIwJ/tZv349Vq9eDbfbjerqavh8\nPmzcuDHWT2zcuBHFxcW49tprce2112L16tXGahU/kkZyaK1Nl0AWMCcZmJMMqZ7TxY5mmXLq1Cls\n2bIF27Ztiz123333Yd26dXjooYcAAHv37sVjjz2Gj370o6bKjBE/kkZypPLtRFIJc5KBOcnAnOzl\n+eefR2lpKVauXBl7bM2aNejq6sJPfvITAJEm7dprrzVUYTwlvcv3+Xy6oaHBdBlEREQp7dChQ7jq\nqqtMl3HRwuEw5s2bh3vvvRdPPPFE3HOrVq1Cf38/tm7dijlz5qCkpARpaWnweDzYsWPHBb/XRD8r\npdRurbXPynnET3cODAyYLoEs2rNnT8ovok0FzEkG5iQDc7KPrVu34vjx47juuuvQ8PsGDIWHMBQe\nQjAcRPV11fjyF76M+vp6zJ49G3v37jVdLoAUaNKCwaDpEsiis2fPmi6BLGBOMjAnGZiTGVrrSBMW\nGoI/5MdQaAhf/cZXAQB/8Rd/Me7rHnzwQSxcuDBZZU5KfJNGREREM1MwHIxrxIb/HAoPxV204Uhz\nYP1318OV5kKGIwMuR+TPDEcG0lRkeX5PTw+++c1voq+vz9THGUN8k+Z2u02XQBbV1taaLoEsYE4y\nMCcZmNOlC+swAqEA/CF/pAkLn2/GQuFQ7DilFJxpTrgcLuRk5MDlcMWasfS0ydsdt9uNffv24f3v\nf/90fpwLIr5JC4VCkx9EttDV1QWPx2O6DJoEc5KBOcnAnKzRWiOoxxkVCw3FHZuelo4MRwY8GZ74\nUbG0jEu6mjYYDOKVV1651I8ypcQ3aX6/33QJZFFzczO8Xq/pMmgSzEkG5iQDc4oX1uGEjZg/5EdY\nh2PHKaWQ4chAZnomPBmeWCPmcrjgSJue2zcNDQ3B5XJNy7kvlvgmjYiIiOxDa41gOHh+ejK6Rswf\n9CMQDsQd60xzIsORgctcl8WNijnTnNxjDinQpNmt66Xx2fG+aDQWc5KBOcmQyjmFwqG49WEjpydH\njoqlqTRkODLgdrrHTE9O16jYxcjIyDBdwhjimzQ73rWeEsvNzTVdAlnAnGRgTjJIzykUDuFk30k0\nn2tGZiATJ3tPxhqyYDh+CyynI7Jo3+10Rxbtp51ftC9hVMyO/UTSmzSlVBqAnwGoBKABPKi1/tmI\n5xcDeAXAZQDeAPDPWo9oyUfp7++f3oJpyuzZsyfuVhxkT8xJBuYkg5SczvnPobm7Gc3nmuP+PNF9\nAkPhyML9ry38GnL9uchIz0COM2fcrSykGhgYsF1TbWIkTQP4sNb6lFLqVgBPINK0DftPAJ8GsA3A\n/wFwF4DXk14lERFRCgmEA2jtaT3fiI1oxroGu2LHpat0lOeWw5vnxY1lN8Kb54XX44XrjAvV+dUi\nRsVSRdKbNB3ZXe5U9NtKAHuGn1NKzQFQpbX+afT7VwDcigmatPR08TO2M0ZBQYHpEsgC5iQDc5Ih\n2TlprdE12JVwVKy1pxVBfX6KMj8zH16PF++qeBe8Hm+sGSvLLYMzzTnm3Ie6DqV0g8bpziil1KcA\nPAzgTwDeN+KpcgAnRnzfCuCOBK9/AMADAFBaWoq6ujoAkQWaubm52LMn0vcVFBRg0aJFsZujpqen\nY/ny5WhsbER3dzcAwOfzoaOjAy0tLQCA+fPnw+VyYf/+/QCAwsJCLFiwAPX19QAiFyosW7YMDQ0N\n6O3tBQAsXboUra2taGtrAwBUV1fD4XDg4MGDAIDi4mJUVVVh586dAICsrCwsXboUu3btit17dNmy\nZWhqakJ7ezsAYOHChQiFQjh8+DAAoKysDOXl5di1axcAICcnBz6fDzt37oxtQ7J8+XIcOXIEnZ2d\nAIDFixfD7/fj6NGjAICKigoUFRVh+Ib0Ho8HtbW1qK+vj91e66abbsKBAwdw5swZAEBNTQ16enpw\n7NgxAIDX60V+fj4aGxsBALNmzUJNTQ22b98OrTWUUlixYgX27NkTux1KbW0turq6cObMGdTV1TEn\n5sScmBNzusScAjqAUG4IOl9jx74d6Ah04HToNE6HT6NnqAfDXA4Xil3FmIVZWJC7ADVza1CZW4m+\n1j6409zxOZ0GOrI64F3qTZjT4OAgenp6kJmZCa11LAOn04mMjIzYTv1paWnIzs5Gb29vbNf/nJwc\nDA4Oxn7mic7hdDpjS5iGz9HTc/6z5OTkYGBgILY/alZWFkKhEIaGItOxGRkZSE9Pj53D4XDA7XbH\nnSM3Nxf9/f2xc7jdbgSDwdg5/H4/HA5H7LM7HA5kZWXF/r0fPkdfXx/C4XDsHIFAAIFA5MpVl8uF\nUCgU601G/z5dCDXytgnJppRaBeBJAFdprbVSaimAr2itb4w+fyuAB7TWq8Y7R3V1tR7+hSZ7q6ur\nE7E2Y6ZjTjIwJxkuJSetNTr6OxKOip3sPQmN8///LnIXxUbCqvKqYiNjJdklU7ZW7NChQ7jqqqum\n5Fx21NPTM2Vr0ib6WSmldmutfVbOY3SuUGv930qprwMoAHAakWnQshGHlANoMVEbERFRMvQH+hM2\nYs3dzRgIDsSOy0rPgtfjxTVzrsHdl98da8oqPZVwO3mLxFRk4urOeQD6tdbtSqllAAa11qcBQGt9\nQinVp5RaCeBXAD4E4JFJzjfdJdMU4fpBGZiTDMxJhuGcQuEQTvWdGtOMNXU3obO/M3a8gkJpTim8\neV4sKVoSt1as0F3I/+dNkfb2dlRUVKCgoAAtLS1wOseuwbMDE7/llwHYqpRyAOgE8FdKqT8HcLnW\n+isA7gPwUvS4F7XWE07i5uTkTHe9NEWWL19uugSygDnJwJzsqXuoO35ELNiMpzc/HbeVBQDkZuSi\nylOF60uuj2vE5nrmwuXgJu3TbdOmTVixYgWOHj2KzZs345577rHd9huAmas7GwEsGPXw7lHPX231\nfNwnTY7GxkbU1taaLoMmwZxkYE7mBMIBtPW0xY2KNZ1rGrOVhUM5MMc5B1cWXonlZcvjmrH8zHyO\nihkSDoexYcMGrFu3DocOHcJzzz2He+65B319fcjOzjZdXhzx4+XDV2iQ/Q1fsUT2xpxkYE7TS2uN\ns/6zY6Ymm8+Nv5XFyoqVkUYs2oyV55bjzR1v8gIPm9m2bRtOnz6NVatWoaWlBU899RSOHTuGOXPm\nmC5tDPFNGhER0cXyh/w40X1izIL95nPN6B463wg705yo9FTiisuuwM2VN8eNiuW58gx+AsN++mmg\nfV/y37f4auC2py7qpevXr8fq1avhdrtRXV0Nn8+HjRs34jOf+QwAYOPGjXjkkUdQUlICrTWqqqrw\n5S9/GQsWjJ4EnH7imzS7DU3S+Hw+S1cck2HMSQbmZJ3WGp39nfHTk9FRsVN9p+JuBl6YVQhvnhe3\nem+NNWHePC9Ks0sv6mbgzMleTp06hS1btmDbtm2xx+677z6sW7cOn//85wEAe/fuxec+9zn80z/9\nEwDg29/+Nu68807s378/6RcYiG/ShjePI/vr6OjghR4CMCcZmNNY/YF+HO8+PmZ68nj3cfQHz69f\nzkrPQqWnElfPvhp3Xn5n3KhYtnNq/+Kf8jld5GiWKc8//zxKS0vjpqDXrFmDj3/843jttdewZs0a\n7N27F6tWnd+e9UMf+hC++MUv4q233sLVV1teMj8lxDdpw7sEk/21tLTg8ssvN10GTYI5yTBTcwrr\ncGQri1EL9pvPNaOjvyN2nIJCSXYJvHleXFd4XdxGr4XuwqTdDHym5mRH4XAYGzduxNq1a+Mu2sjP\nz8cdd9yBjRs3Ys2aNdi3bx8WL14c99qsrCx0dXWNPuW0E9+kERFR6ukZ6hnbiHU340T3CfhD/thx\nOc4ceD1evKP4HXEjYpWeSmSmZxr8BGQ3W7duxfHjx7FkyZLYLdCG3XDDDXj44YdRX1+PjIwMzJ49\nO/ac1hpNTU2YP39+skuW36RlZvKXUAoT/4LThWNOMqRCTsFwEG29bQlHxc4Mnokd51AOlOWUwZvn\nxbKSZXGjYgWZBbbeyiIVckoV69evBwCsXr163GMefPDBMVOa3/3ud1FTU4PS0tJprS8R8U2anX85\nKZ7LxQ0aJWBOMkjK6ezg2THrxJq7m9HS04Jg+PxWFpe5LoPX48WN5TfGRsWqPFWoyK2A02HPHeEn\nIymnVLd58+YJnw8EAnj66afR2Xn+DhB1dXV49NFH8eqrr053eQmJb9KG71RP9rd//37uFyQAc5LB\nbjkNhYbQ0tMyphFr7m7GOf+52HHpaemYmzsXVZ4qvKviXXE3BL8s8zKDn2B62C0nGt/g4CD27duH\nuro6bN++HVprLFiwAG+88QYWLVpkpCbxTRoRESWH1hqnB06PmZps7m5GW29b3FYWs7Nmw+vx4pbK\nW+IasdKcUqSn8X89ZE+vvPKK6RLiiP9NsetNUWmswsJC0yWQBcxJhunMaSA4gBPdJ+JHxKJ/9gX6\nYsdlOjJR6anEwoKFuL3q9tj0ZKWnEjkZKbztxAXg75Mc6en2a4nsV9EF4ny/HCZ2a6YLx5xkuNSc\nwjqM9r722PTk8e7jsUbsVN+puGNLskvg9Xhx1+V3xa0VK8ouStpWFlLx90kOO16IKL5J6+3tNV0C\nWVRfX8+1GQIwJxms5tQ71JtwevJE9wkMhgZjx2U7s+H1eFFbVBvXiM31zEVWetY0fpLUxt8nOXp7\ne5Gbm2u6jDjimzQiopkuGA7iZO/JhM3Y6YHTsePSVFpkKwuPF0tLlsatFZudNZtXyxPZjPgmLS2N\nQ+1ScGpaBuZkX28Pvh1rxH7d/Wu89n9ei21lEQifv0VenisPXo8X7yx9Z2xEzJvnRUVuBTIcGQY/\nwczD3yc57PiXFPFNGm+wLseyZctMl0AWMCezAqEAWnpaEi7af9v/duy49LR0VIQr4PV4saJiRawR\n83q8mJU5y+AnoJH4+ySHHe+xKr5J6+/vn/wgsoWGhgb4fD7TZdAkmNP001rjzOCZMVOTzeciW1mE\ndCh2bEFmAbx5Xrxn7ntiU5PePC/aD7dj6TuWGvwUZAV/n+To6+uz3cCP+CYtFApNfhDZAi/ykIE5\nTZ3B4GDkqslRjVhzdzN6A+d/zi6HC3M9c1GdX433ed8X14zlZiReyNzU15Ssj0GXgL9PcoTD4ckP\nSjLxTRoRkUlhHUZnf2fCUbFTfaegoWPHFrmL4M3z4o55d8Q1YiXZJdzKgojGEN+k2W1oksa3dCmn\nZiRgTon1BfoSjogd7z6OgeD529O5092o9FSiprAGH/B8ILZOrNJTCbfTPWX1MCcZmJMc2dnZuP/+\n+/HWW2/hN7/5DQBg5cqVKC4uxve+9z0jNYlv0gKBwOQHkS20trZi/vz5psugSczknELhEE72nRzT\niDWfa0bnwPmbLqepNJRml8Kb54WvyBc3KjYna05SrhKbyTlJwpzsR2uNefPm4fTp0zh16lTsgoGh\noSHDlY0lvkmz4w+VEmtra+N/rASYCTmd859LOD15oudE3FYWngwPvHleXF96/flGzONFhacCLofZ\nrRVmQk6pgDnZT11dHU6ePAmXy4VXX30V999/PwB7DvqIb9KIiBIJhCNbWSQaFTvrPxs7Ll2lozy3\nHN48L24qvyk2PenN82KWa5Yt904ioov3wgsvYPny5cjJycGLL74Ya9LsSHyTZsd7bVFi1dXVpksg\nCyTlNLyVxZhGrLsZrT2tcVtZ5Gfmw+vx4t1z3x1rwrweL8pyy+BMcxr8FBdHUk4zGXOyl56eHvzo\nRz/CV7/6VeTm5uLee+/FsWPHMG/ePFtuPCy+SePfcuVwOBymSyAL7JiTP+SPuwH4yD97Aj2x4zLS\nMjDXMxcLZi3AeyvfG7doP8+VZ/ATTD075kRjpXpOX/rtl/BW11tJf98r86/Ew3/28AW/7gc/+AEC\ngQBWr16NzMxMZGVl4aWXXsJjjz1my35CfJM2MDAw+UFkCwcPHkRhYaHpMmgSpnLSWqOjvyPhFZQn\ne0/GbWVR6C5ElacKt8+7PW5UrCS7BI601P6f4jD+PsnAnOzlhRdewM0334yCggIAwJ133omXX34Z\nX/jCFzA4OGi4urHEN2lEJEt/oD9hI9bc3Ry3lUVWeha8Hi+umX0N7rr8rrhmbCq3siCii3cxo1mm\nHD16FG+++SY2bdqEYDAIAPjc3V23AAAgAElEQVTLv/xLfP/738f//M//4B3veIfhCscS36Q5nfLW\nksxUxcXFpksgC6Yip1A4hFN9p8Y0Y03dTejsP7+VhYJCaU4pvB4vaotq4xqxIneRLacf7IK/TzIw\nJ/t44YUXAAAf+chH8JGPfCTuuRdffNGW91kV36TZcaEfJVZVVWW6BLLgQnLqHuoeMyLWdK4JJ7pP\nYCh8fnuc3IxcVHmqcH3J9XGN2FzPXONbWUjF3ycZmJM9hMNhfPvb38Zdd92FRx99NO65Z555Bj/6\n0Y/w7LPPGqpufOKbNN4XTY6dO3di5cqVpsugSYzOKRAOoK2nbUwj1tzdjK7Brthxsa0sPF4sL1se\n14zlZ+ZzVGyK8fdJBuZkDz//+c/R2tqKjRs3jrnh/Sc+8Ql85zvfwXe+8x1D1Y1PfJNGRJdOa42z\n/rNoPteMnT070djQiKbuJjSfi2xlEdTB2LHDW1msrFgZ29zVm+dFeW65yK0siCj1vfDCCygtLcUt\nt9wy5rlrr70WPp8Pr7zyChYsWGCguvGJb9LS0nhTYimysrJMlzDjDYWGcKL7RGyh/shd97uHumPH\nOd92otJTiSsuuwI3V94cNyqWaltZSMXfJxmYkz1Mdu/N3/3ud+jt7Y3dImpYXV3dNFY1OfFNGm+w\nLgdvNJwcWmt09nfGT09GR8VO9Z1CWIdjxxZmFcKb58Wt3lvjdtovzS6dMVtZSMXfJxmYkxyjGzQ7\nEN+k9fX1mS6BLNq1axf/gzWF+gP9kQ1eR1w52XyuGce7j6M/2B877kK3sti1axcqllYk86PQReDv\nkwzMSY5EI2mmiW/SwuHw5AeRLXDj4QsX1uHIVhbnxk5PdvR3xI6byq0smJMMzEkG5iSH1nryg5JM\nfJNGlAp6hnrGNmLdzTjRfQL+kD92XK4zF948L/6s+M/ipifn5s5FZjrvY0tElErEN2l2G5qk8dlx\no8BkCoaDaOttSzgqdmbwTOw4h3LEtrK4oeSGuGasILNg2reymOk5ScGcZGBOcthxjbv4Js3v909+\nENlCU1MTrrzyStNlTLuzg2fHrBNr7m5GS08LguHzW1nMcs2CN8+Lm8pvimvEKnIq4HSY28pipuQk\nHXOSgTnJ4ff7bXc1rvgmLRAImC6BLGpvb0+Z/1gNhYbQ0tMyphFr7m7GOf+52HHONCfm5s7FvLx5\neHfFu2PNWFVelW23skilnFIZc5KBOckxfD9POxHfpBFNF601Tg+cHjM12dzdjLbetritLOZkzYE3\nz4v3Vr43NiJW5alCaQ63siAioosjvkmz29AkjW/hwoWmS0hoIDiAE90n4kfEon/2Bc5v8ZLpyESl\npxILCxbi9qrbY41YpacSORmpszbSrjlRPOYkA3OSIzPTfhdfiW/S7HjJLCUWCoWMvXdYh9He1x6b\nnjzefTzWiJ3qOxU7TkGhJLsE3jxv3J5iVZ4qFGUXIU2l/h0uTOZE1jEnGZiTHHbsJ8Q3aYODg6ZL\nIIsOHz6MkpKSaX2P3qFeHO8+jmPnjsWNiJ3oPoHB0Pl/V3KcOfB6vFhStCRuT7FKT+WM38oiGTnR\npWNOMjAnOfx+PzIyMkyXEUd8k0YzTzAcxMnek2PWih3vPo4/DfwpdlyaSkN5Tjm8eV5cX3J93KL9\nZGxlQUREdCnEN2l263ppfGVlZRd0/NuDbydctN/S04JA+PxVvZe5LoPX48U7y94ZNz1ZkWt2Kwup\nLjQnMoM5ycCc7Km9vR0VFRUoKChAS0sLnE4nnE77/f9CfJNmxx8qJVZeXj7msUAogJaeloSL9t/2\nvx07Lj0tHXNz58Lr8WJlxcrYiJjX48VlmZcl82OkvEQ5kf0wJxmYkz1t2rQJK1aswNGjR7F582bc\nc889thz0Ed+k8Qbr9qe1xpnBM3ht+2u4bN5lcc1YW28bQvr8wtrZWbPh9Xhxc+XNcY1YaU4p0tPE\n/+sqwq5du7By5UrTZdAkmJMMzMl+wuEwNmzYgHXr1uHQoUN47rnncM8996Cvrw+5ubmmy4vD/+vR\nlBkMDkaumhwxGjb8Z2+gN3JQB+ByuFDpqcSV+Vfi1qpbY81YpacSuRn2+gUhIqLUsm3bNpw+fRqr\nVq1CS0sLnnrqKRw7dgxz5swxXdoY4ps0h4MbhSaT1hod/R1j1ok1n4tsZaFx/hLm4uxieD1evH/e\n++HN8yLQEcB7fe9FcXbxjNjKQireD1cG5iRDqufU/uST8B96K+nv67rqShR/9rMX9dr169dj9erV\ncLvdqK6uhs/nw8aNG/HII48AQOyfS0pKcO7cOTz88MP42Mc+NpXlWya+SXO73aZLSEl9gb6EI2LH\nu49jIDgQO86d7oY3z4trC6/FB/I+gCpPFbx5XszNnQu3c1Q2VyX5Q9BF8fl8pksgC5iTDMzJXk6d\nOoUtW7Zg27Ztscfuu+8+rFu3Dl/84hcBAHv37sVnPvMZ/Mu//Av27t2L66+/Hg888ADS0pI/uCC+\nSeOatIsXCodwsu/kmEas+VwzOgc6Y8elqTSUZpfCm+eFr8gXWyfmzfNiTtYcy1tZ7Ny5E8uWLZuu\nj0NThDnJwJxkSPWcLnY0y5Tnn38epaWlcesE16xZg49//OP4/ve/j3vvvRd79+7FHXfcAQCoqqqC\n0+k0tmWT+CYtHA5PftAMd85/LuGo2InuExgKD8WO82R4InuKlV5/vhHzeDHXMxcZjku/6sXv91/y\nOWj6MScZmJMMzMk+wuEwNm7ciLVr18Y1Xfn5+bjjjjvwwgsv4N5778W+fftw5ZVXAgC+/vWv48kn\nn2STRpcmEI5sZTG8qevIZqxrsCt2XLpKR4WnAl6PFzeW3Rjb4NWb58Us1yxu8EpERClp69atOH78\nOJYsWYL9+/fHPXfDDTfg4YcfRn19Pc6dO4e7774bJ0+exPz58/GrX/3KUMWAsuO9qi7EkiVL9O7d\nu02XkRTDW1mMmZ7sbkZrT2vcVhYFmQVxO+wPN2JlOWXGtrIIBoNIT+ffC+yOOcnAnGRIpZwOHTqE\nq66Su7j47rvvxhtvvDHhMddddx1yc3Oxfft2nDt3DjU1NdiwYQNuueUWHD16FE899RTOnTuHV199\ndcLzTPSzUkrt1lpbWqwo/t+cVBxK9of8cTcAH9mM9Qz1xI5zOVyY65mLBbMW4L2V7401Y5V5lfBk\neAx+gsSOHDmChQsXmi6DJsGcZGBOMjAn+9i8efOEzw8MDOCZZ55BR0cHACAvLw8f/vCHsWXLFtxy\nyy2YP38+nn/+edxzzz3JKBdACjRpgUBg8oNsaHgri0RrxU72nozbyqLIXQRvnhe3V90eNypWkl0i\naiuLzs5O/sdKAOYkA3OSgTnJEQwGsW/fPtx6662xx+6++26sWbMGzzzzjJGaxDdpdtcf6E/YiDV3\nN8dtZZGVngWvx4tr5lyDuy+/OzZVWempHLuVBREREU25V155Je77JUuW4OjRo4aqSYEmLSsry3QJ\nCIVDONV3akwz1tTdhM7+81tZKCiU5kS2slhStCQ2Iub1eFHoLkz5RfuLFy82XQJZwJxkYE4yMCc5\nMjMzJ3z+T3/6Ex599FH8/ve/xxNPPBHb/HY6iW/SknnhQ/dQ95gRsaZzTWO2ssjNyEWVpwrXl1wf\n14jN9cyFy+FKWr12k4rrB1MRc5KBOcnAnOSYrJ+YM2cOvvWtbyWpmgjxTdrg4OCUni8QDqCtp21M\nI5ZoK4vy3HJ4PV4sL1se14zlZ+an/KjYxTh69CjKyspMl0GTYE4yMCcZmJMcfr8fGRmXvifoVBLf\npF0MrTXO+s+OmZpsPhfZyiKog7Fj8zPz4fV4sbJiZWxzV2+eF+W55XCmOQ1+CiIiIkpl4pu0ibre\nodAQTnSfiC3UH3lT8O6h7thxzjQnKj2VuOKyK3Bz5c1xo2J5rrxkfIwZoaKiwnQJZAFzkoE5ycCc\n5HA67TfwIr5Jczqd6OiL38pieFTsVN8phPX520YVZhXCm+fFrd5b43baL80uhSPNYfBTzAxFRUWm\nSyALmJMMzEkG5iQHm7RpcPjsYdz86s2x74e3srh69tW48/I740bFsp3ZBiulhoaGuJvakj0xJxmY\nkwzMSY7+/n7k5uaaLiOO+CYt25GNR5Y+EmvEitxFXLRPRERE4olv0mZnzMaaK9eYLoMs8Hjsd6sq\nGos5ycCcZGBOcqSl2e8OPvar6AK53dyNX4ra2lrTJZAFzEkG5iQDc5IjO9t+S6LEN2m9vb2mSyCL\n6uvrTZdAFjAnGZiTDMxJjp6eHtMljCG+SUvmHQfo0gSDwckPIuOYkwzMSQbmRJdCfJNGREREdCHa\n29vhdDpRXFyMQCBgupxxiW/S7Ha5LI3vpptuMl0CWcCcZGBOMjAne9q0aRNWrFgBl8uFzZs3AwBy\ncnIMVzWW+CZtYGDAdAlk0YEDB0yXQBYwJxmYkwzMyX7C4TA2bNiA+++/H2vXrsVzzz0HwJ79RNKb\nNKVUplLqOaXUYaXUcaXUx0c9/6JSqk0p9cfo19yJzsf5fjnOnDljugSygDnJwJxkYE72s23bNpw+\nfRqrVq3Chz/8Yfzyl7/EsWPHEAqFTJc2hol90rIB/AzARwEUADiglHpVa90y4ph7tdZ1BmojIiIi\ni371gyM43ZL8XRZmV+Tgxr9ccFGvXb9+PVavXg23243q6mr4fD5s3LgRn/nMZ2LHvP766/jSl76E\nvr4+DA4O4p577sGTTz45VeVblvQmTWt9BsCPot+eVkq1ALgMQMv4r4qnlHoAwAMAUFJSgrq6OgDA\nvHnzkJubiz179gAACgoKsGjRIuzYsQMAkJ6ejuXLl6OxsRHd3ZEbrPt8PnR0dKClJfL28+fPh8vl\nwv79+wEAhYWFWLBgQewyapfLhWXLlqGhoSG2/cfSpUvR2tqKtrY2AEB1dTUcDgcOHjwIACguLkZV\nVRV27twJAMjKysLSpUuxa9eu2PDqsmXL0NTUhPb2dgDAwoULEQqFcPjwYQBAWVkZysvLsWvXLgCR\nuXOfz4edO3fC7/cDAJYvX44jR46gs7MTALB48WL4/X4cPXoUQORGv0VFRWhoaAAQ2WSxtrYW9fX1\nsRHJm266CQcOHIj97a+mpgY9PT04duwYAMDr9SI/Px+NjY0AgFmzZqGmpgbbt2+H1hpKKaxYsQJ7\n9uzB2bNnAUT2Cerq6kIoFEJdXR1zYk7MiTkxJ4E5DQ4OoqenB5mZmdBaw+/3IzAUQDgcRlqaQigU\nvVe2AhxpjriRKYfDgXA4HNuRIbJxrEY4HPleKQWVphCe9BwhaA0EhgIIBoMIhUIYGhoCAGRkZCA9\nPR39/f2x491ud9zWGr29vdiyZQtef/119PT0wO12495778WTTz6JT37yk/D7/fjv//5v/Pu//zu+\n+93voqqqCkopPPvss7Hz5Obmoq+vD+FwpFa3241AIBC7AMHlcsVyT5TThVAmt7BQSi0G8D0AV+to\nIUqpDQDeC6AXwCat9dMTneOaa67Re/funfZa6dKdOHECc+dOOHtNNsCcZGBOMqRSTocOHcJVV11l\nuoxL8vjjj2PDhg1obm6O3UKyq6sLJSUlePnll3HXXXehuroav/jFL7BgwcWN1AET/6yUUru11j4r\n5zF24YBSajaAbwP4az2iU9Ra/53WuhLArQD+Til183jnABD72xTZ3/DfSsnemJMMzEkG5mQf4XAY\nGzduxNq1a+Pu8Z2fn4877rgDGzZswA9/+EMsXLjwkhq0qWTk3p1KqVkAfgzgs1rr3yU6RmvdopTa\nAmAxgF8ksz4iIiJKLVu3bsXx48exZMmS2JTxsBtuuAEPP/ww8vPzcd111xmqcKykN2lKKQ+ANwA8\nobX+aYLnr9Ba/1EpVYDIaNpHJzqfy+WankJpynm9XtMlkAXMSQbmJANzso/169cDAFavXj3uMa++\n+ioeeuihZJU0KRPTnQ8CqAXwtRHbbHxCKfXJ6PNfV0o1A/g1gG9prd+c6GQOh2N6q6Upk5+fb7oE\nsoA5ycCcZGBO9rF582Zorcf9CgaD+O1vf4sf/vCHOHXqFABgaGgo1tyZkPQmTWv9uNY6W2t9xYiv\np7XWX4k+f7vW2qu1rtZaf2Oy8w1fxUH2N3xlFNkbc5KBOcnAnOTo7++Hz+fD448/jttuuw3XXHMN\nrrnmGrS2thqryciaNCIiIiI7+uAHP4gPfvCDpssAkAK3hUpPZ58pxaxZs0yXQBYwJxmYkwzMSQ47\nLp8S36RlZWWZLoEsqqmpMV0CWcCcZGBOMjAnOdxut+kSxhDfpI3cSZjsbfv27aZLIAuYkwzMSQbm\nJIcd+wnxTRrJYfLuFmQdc5KBOcnAnOhSsEmjpBm5wzPZF3OSgTnJwJzoUohv0nJzc02XQBatWLHC\ndAlkAXOSgTnJwJzksGM/Ib5JGxgYMF0CWbRnzx7TJZAFzEkG5iQDc5LDjvuuim/SgsGg6RLIorNn\nz5ougSxgTjIwJxmYkxyhUMh0CWOIb9KIiIiIUpH4Js2O+5pQYrW1taZLIAuYkwzMSQbmJIcd+wnx\nTZodhycpsa6uLtMlkAXMSQbmJANzksOOy6fEN2l+v990CWRRc3Oz6RLIAuYkA3OSgTnZU3t7O5xO\nJ4qLixEIBAAAQ0NDhqsaS3yTRkRERHQhNm3ahBUrVsDlcmHz5s2myxmX+CbN5XKZLoEsmjdvnukS\nyALmJANzkoE52U84HMaGDRtw//33Y+3atXjuuecAABkZGYYrGyvddAGXyo53rafE7LhRII3FnGRg\nTjKkek7/8+Jz6Dx+LOnvW1g5D++6/4GLeu22bdtw+vRprFq1Ci0tLXjqqadw7NgxzJ07d4qrvHTi\nR9LsuPkcJcZNHWVgTjIwJxmYk/2sX78eq1evhtvtRnV1NXw+HzZu3BjbHH/9+vX46Ec/arjKCPEj\naURERGTGxY5mmXLq1Cls2bIF27Ztiz123333Yd26dXjooYcAAHv37sXVV19tqsQ44kfS0tPZZ0pR\nUFBgugSygDnJwJxkYE728vzzz6O0tBQrV66MPbZmzRp0dXVh69atAIB9+/axSZsqWVlZpksgixYt\nWmS6BLKAOcnAnGRgTvYRDoexceNGrF27Fkqp2OP5+fm444478NJLLwEA9u/fzyZtqvT09JgugSza\nsWOH6RLIAuYkA3OSgTnZx9atW3H8+HEsWbIE+/fvj/u64YYb8POf/xy/+tWvkJWVhfz8fNPlAuCa\nNCIiIpoB1q9fDwBYvXr1uMc8+OCDthlFA1KgSRs5ZEn2xvWDMjAnGZiTDMzJPibbtLanpwff/OY3\ncebMmSRVNDnx0505OTmmSyCLli9fbroEsoA5ycCcZGBOcuTm5mLfvn14/vnn4fV64fV6ce211xqt\nSXyTxn3S5GhsbDRdAlnAnGRgTjIwJzn6+vrwyiuvoKurC83NzWhubsYf/vAHozWJb9JCoZDpEsii\n7u5u0yWQBcxJBuYkA3OSIxwOmy5hDPFNGhEREVEqEt+kZWdnmy6BLPL5fKZLIAuYkwzMSQbmJIfb\n7TZdwhjim7RAIGC6BLKoo6PDdAlkAXOSgTnJwJzksGM/Ib5JGxoaMl0CWdTS0mK6BLKAOcnAnGRI\ntZy01qZLmDZT1aRN5c9IfJNGRERE08/pdGJgYMB0GbY3MDAAp9M5JecS36RlZmaaLoEsmj9/vukS\nyALmJANzkiGVciosLERbWxv6+/tTckTN5XJd0uu11ujv70dbWxsKCwunpCbxWyHzjgNyXOovACUH\nc5KBOcmQSjl5PB4AwMmTJ225futShUIhOByOSzqH0+lEUVFR7Gd1qcQ3aRx6lWP//v1YuXKl6TJo\nEsxJBuYkQ6rl5PF4pqwBsZu6ujrbZSV+upOIiIgoFYlv0qZqcR5Nv6mao6fpxZxkYE4yMCc57JiV\nkr74b8mSJXr37t2myyALgsEg0tPFz7CnPOYkA3OSgTnJkayslFK7tdaWdjkWP5LW29trugSyqL6+\n3nQJZAFzkoE5ycCc5LBjVuKbNCIiIqJUJL5JS0sT/xFmjFS6FD2VMScZmJMMzEkOO2Ylfk2az+fT\nDQ0NpssgIiIimtSMWpPW399vugSyiM20DMxJBuYkA3OSw45ZiW/SQqGQ6RLIIl7kIQNzkoE5ycCc\n5LBjVuKbNCIiIqJUJH5NWm1trW5sbDRdBlkwMDCArKws02XQJJiTDMxJBuYkR7KymlFr0lLxJq+p\nqrW11XQJZAFzkoE5ycCc5LBjVuKbtKGhIdMlkEVtbW2mSyALmJMMzEkG5iSHHbMS36QRERERpSLx\nTVpmZqbpEsii6upq0yWQBcxJBuYkA3OSw45ZiW/SlFKmSyCLHA6H6RLIAuYkA3OSgTnJYcesxDdp\nAwMDpksgiw4ePGi6BLKAOcnAnGRgTnLYMSvxTRoRERFRKhLfpDmdTtMlkEXFxcWmSyALmJMMzEkG\n5iSHHbMS36TZ8a71lFhVVZXpEsgC5iQDc5KBOclhx6zEN2l2vNcWJbZz507TJZAFzEkG5iQDc5LD\njlmJb9KIiIiIUpH4Ji0tTfxHmDF4/zoZmJMMzEkG5iSHHbMSf4N1n8+nGxoaTJdBRERENKkZdYP1\nvr4+0yWQRbt27TJdAlnAnGRgTjIwJznsmJX4Ji0cDpsugSzixsMyMCcZmJMMzEkOO2YlvkkjIiIi\nSkXi16QtWbJE796923QZZIHf7+e+dgIwJxmYkwzMSY5kZTWj1qT5/X7TJZBFTU1NpksgC5iTDMxJ\nBuYkhx2zEt+kBQIB0yWQRe3t7aZLIAuYkwzMSQbmJIcdsxLfpBERERGlIvFNmh03n6PEFi5caLoE\nsoA5ycCcZGBOctgxK/FNmvQLH2aSUChkugSygDnJwJxkYE5y2DEr8U3a4OCg6RLIosOHD5sugSxg\nTjIwJxmYkxx2zEp8k0ZERESUisQ3aRkZGaZLIIvKyspMl0AWMCcZmJMMzEkOO2YlvklzOp2mSyCL\nysvLTZdAFjAnGZiTDMxJDjtmlfQmTSmVqZR6Til1WCl1XCn18VHPL1ZK7Yk+96xSasIaeYN1Oex4\n81oaiznJwJxkYE5y2DErEyNp2QB+BuBKAEsAfFopVTHi+f8E8GkA8wBcA+CupFdIREREZFjSmzSt\n9Rmt9Y90xGkALQAuAwCl1BwAVVrrn2qtQwBeAXDrROdzOBzTXjNNjZycHNMlkAXMSQbmJANzksOO\nWaWbfHOl1GIAmQD2Rx8qB3BixCGtAO5I8LoHADwAAKWlpairqwMAzJs3D7m5udizZw8AoKCgAIsW\nLcKOHTsAAOnp6Vi+fDkaGxvR3d0NAPD5fOjo6EBLSwsAYP78+XC5XNi/P1JSYWEhFixYgPr6egCA\ny+XCsmXL0NDQgN7eXgDA0qVL0draira2NgBAdXU1HA4HDh48CAAoLi5GVVUVdu7cCSCyAe/SpUux\na9cuDAwMAACWLVuGpqam2G0pFi5ciFAoFLskuKysDOXl5bHh2JycHPh8PuzcuTN2/9Lly5fjyJEj\n6OzsBAAsXrwYfr8fR48eBQBUVFSgqKgIDQ0NAACPx4Pa2lrU19cjGAwCAG666SYcOHAAZ86cAQDU\n1NSgp6cHx44dAwB4vV7k5+ejsbERADBr1izU1NRg+/bt0FpDKYUVK1Zgz549OHv2LACgtrYWXV1d\n6O3tRV1dHXNiTsyJOTEn5mSrnJqbmwEAJ06cmPacLoQytRmsUmo2gJ8DeEBr/bvoY0sBfEVrfWP0\n+1ujz68a7zxXXXWVPnToUDJKpku0c+dOLFu2zHQZNAnmJANzkoE5yZGsrJRSu7XWPivHGrm6Uyk1\nC8CPAXx2uEGLOgVg5DWw5YhMh44rHA5PfYE0LYb/RkX2xpxkYE4yMCc57JiVias7PQDeAPCE1vqn\nI5/TWp8A0KeUWqmUcgD4EIAfJrtGIiIiItOSPt2plPocgM8gMmo27L+itXxFKVUL4CVELiZ4UWv9\n6ETnW7Jkid69e/e01UtTJxgMIj3d6DJIsoA5ycCcZGBOciQrK1tPd2qtH9daZ2utrxjx9bTW+ivR\n5xu11ldrrSsma9AAew5PUmJHjhwxXQJZwJxkYE4yMCc57JiV+DsOBAIB0yWQRcNX9ZC9MScZmJMM\nzEkOO2YlvkkjIiIiSkXim7SsrCzTJZBFixcvNl0CWcCcZGBOMjAnOeyYlfgmzdQ+b3ThuH5QBuYk\nA3OSgTnJYcesxDdpg4ODpksgi4Z3liZ7Y04yMCcZmJMcdsxKfJNGRERElIrEN2kZGRmmSyCLKioq\nTJdAFjAnGZiTDMxJDjtmJb5Jczqdpksgi4qKikyXQBYwJxmYkwzMSQ47ZiW+Sevr6zNdAlnU0NBg\nugSygDnJwJxkYE5y2DEr8U0aERERUSoS36Q5HA7TJZBFHo/HdAlkAXOSgTnJwJzksGNWSb/B+lTz\n+XzajkOURERERKPZ+gbrU623t9d0CWRRfX296RLIAuYkA3OSgTnJYcesxDdp0kcCZ5JgMGi6BLKA\nOcnAnGRgTnLYMSvxTRoRERFRKuKaNEqacDiMtDT+vcDumJMMzEkG5iRHsrKaUWvSBgYGTJdAFh04\ncMB0CWQBc5KBOcnAnOSwY1bimzQ7ziFTYmfOnDFdAlnAnGRgTjIwJznsmJX4Jo2IiIgoFYlv0txu\nt+kSyKKamhrTJZAFzEkG5iQDc5LDjlmJb9JCoZDpEsiinp4e0yWQBcxJBuYkA3OSw45ZiW/S/H6/\n6RLIomPHjpkugSxgTjIwJxmYkxx2zEp8k0ZERESUisQ3aS6Xy3QJZJHX6zVdAlnAnGRgTjIwJzns\nmJX4Js3hcJgugSzKz883XQJZwJxkYE4yMCc57JiV+Catv7/fdAlkUWNjo+kSyALmJANzkoE5yWHH\nrMQ3aURERESpSHyTlp6ebroEsmjWrFmmSyALmJMMzEkG5iSHHbPiDdaJiIiIkmRG3WDdjpvPUWLb\nt283XQJZwJxkYE4yMLbXu3wAACAASURBVCc57JiV+CaN5JA+ajtTMCcZmJMMzEkOO2bFJo2SRill\nugSygDnJwJxkYE5y2DErrkkjIiIiSpIZtSZtYGDAdAlk0Z49e0yXQBYwJxmYkwzMSQ47ZiW+SQsG\ng6ZLIIvOnj1rugSygDnJwJxkYE5y2DEr8U0aERERUSoS36S53W7TJZBFtbW1pksgC5iTDMxJBuYk\nhx2zEt+khUIh0yWQRV1dXaZLIAuYkwzMSQbmJIcdsxLfpPn9ftMlkEXNzc2mSyALmJMMzEkG5iSH\nHbMS36QRERERpSLxTZrL5TJdAlk0b9480yWQBcxJBuYkA3OSw45ZiW/SHA6H6RLIotzcXNMlkAXM\nSQbmJANzksOOWYlv0vr7+02XQBbZcaNAGos5ycCcZGBOctgxK/FNGhEREVEqEt+kpaenmy6BLCoo\nKDBdAlnAnGRgTjIwJznsmBVvsE5JEw6HkZYm/u8FKY85ycCcZGBOciQrqxl1g/Wenh7TJZBFO3bs\nMF0CWcCcZGBOMjAnOeyYlfgmjYiIiCgViW/SlFKmSyCLuH5QBuYkA3OSgTnJYcesuCaNiIiIKElm\n1Jo07pMmR2Njo+kSyALmJANzkoE5yWHHrMQ3aaFQyHQJZFF3d7fpEsgC5iQDc5KBOclhx6zEN2lE\nREREqUj8mrTa2lptxyFKGqu3txc5OTmmy6BJMCcZmJMMzEmOZGU1o9akBQIB0yWQRR0dHaZLIAuY\nkwzMSQbmJIcdsxLfpA0NDZkugSxqaWkxXQJZwJxkYE4yMCc57JiV+CaNiIiIKBWJb9IyMzNNl0AW\nzZ8/33QJZAFzkoE5ycCc5LBjVuKbNN5xQA6Xy2W6BLKAOcnAnGRgTnLYMSvxTdrAwIDpEsii/fv3\nmy6BLGBOMjAnGZiTHHbMSnyTRkRERJSKxDdpTqfTdAlkUWFhoekSyALmJANzkoE5yWHHrMRvZrtk\nyRK9e/du02WQBcFgEOnp6abLoEkwJxmYkwzMSY5kZTWjNrPt7e01XQJZVF9fb7oEsoA5ycCcZGBO\nctgxq4tqGZVSiwGsAKAAbNda75vSqoiIiIhmuAseSVNK/T8AdgBYCeB2AL9VSv39FNdlWVqa+MHA\nGcOOlzfTWMxJBuYkA3OSw45ZjbsmTSnl1lr3J3i8GcD7tNaHo99/BMA6rXXZdBY6Hp/PpxsaGky8\nNREREdEFmao1aUeUUvcmOj+A8IjvjV550N8/po8km2IzLQNzkoE5ycCc5LBjVhM1aR8E8K9KqZ1K\nqXeMePzLAH6jlPqBUmoLgP8E8NR0FjmRUChk6q3pAvEiDxmYkwzMSQbmJIcdsxq3SdNa7wDgA7AJ\nwBtKqZeVUiVa628CeDeAegDbACzTWj+blGqJiIiIZghL+6QppTwAHgXw1wD+XwBPa63901ybJbW1\ntbqxsdF0GWTBwMAAsrKyTJdBk2BOMjAnGZiTHMnKasr3SdNad2utHwJwPYClAN5SSt1zCTVCKZWl\nlFpwKecAgEAgcKmnoCRpbW01XQJZwJxkYE4yMCc57JjVuE2aUsqtlHpcKbVLKfV7pdRzAAa11ncD\n+DsAn1dKbVdK1VzIGyqlPEqp1wF0APhUgudfVEq1KaX+GP2aO9H5hoaGLuTtyaC2tjbTJZAFzEkG\n5iQDc5LDjllNNJL2PIA7ATyNyFRnMYCfK6WU1voXAK4F8MPoY89dwHuGATwL4F8nOOZerfUV0a8T\nF3BuIiIiopQwUZN2G4BPaq1/oLXeAuA+ANUALgcArXVIa/2N6GMDVt9Qa92rtf4lgODFl31eZmbm\nVJyGkqC6utp0CWQBc5KBOcnAnOSwY1YT3RbqLQAfUkrtBjAI4KMA+gDETdpqrc8C+OcprCkA4CWl\nVC+ATVrrp0cfoJR6AMADAFBSUoK6ujoAwLx585Cbm4s9e/YAAAoKCrBo0SLs2LEDAJCeno7ly5ej\nsbER3d3dAACfz4eOjg60tLQAAObPnw+Xy4X9+/cDAAoLC7FgwYLYPb1cLheWLVuGhoaG2OW6S5cu\nRWtra2yotLq6Gg6HAwcPHgQAFBcXo6qqCjt37gQAZGVlYenSpdi1axcGBiL97bJly9DU1IT29nYA\nwMKFCxEKhXD48GEAQFlZGcrLy7Fr1y4AQE5ODnw+H3bu3Am/P3INx/Lly3HkyBF0dnYCABYvXgy/\n34+jR48CACoqKlBUVBTbC8bj8aC2thb19fUIBiM980033YQDBw7gzJkzAICamhr09PTg2LFjAACv\n14v8/HwMX6wxa9Ys1NTUYPv27dBaQymFFStWYM+ePTh79iwAoLa2Fl1dXfjjH/+Iw4cPMyfmxJyY\nE3NiTrbKqbm5GcFgEIFAYNpzuhAT3XGgGsCLiFwooAE0AfhHrfXWC36XxOe/H8ByrfXfjvN8BYCf\nR9/zF+Odp7q6Wg//i0L2VldXh5UrV5ougybBnGRgTjIwJzmSldWFXN057kha9LZPy5RS2QAyoiNm\nSaO1bolulrsYwLhNGhEREVEqmnQLDq11XzIbNKXUFdE/CwDcCuB3Ex3vdDqTURZNgeLiYtMlkAXM\nSQbmJANzksOOWU20Jm1aKKVyAfweQC6ATKXUSgAPAbhca/0VAF9XSi0E4AfwrNb6zYnOZ8e71lNi\nVVVVpksgC5iTDMxJBuYkhx2zsrSZ7VTSWvdEt9Yo0lrnRf/5tWiDBq317Vprr9a6Onr16ITseK8t\nSmx4YSrZG3OSgTnJwJzksGNWSW/SiIiIiGhy4pu0tDTxH2HG4P3rZGBOMjAnGZiTHHbMytIN1u3M\n5/Pp4X1ViIiIiOxsym+wbmd9fX2mSyCLhjc6JHtjTjIwJxmYkxx2zEp8kxYOh02XQBYN715N9sac\nZGBOMjAnOeyYlfgmjYiIiCgViV+TtmTJEr17927TZZAFfr+f+9oJwJxkYE4yMCc5kpXVjFqTNnzz\nVrK/pqYm0yWQBcxJBuYkA3OSw45ZiW/SAoGA6RLIovb2dtMlkAXMSQbmJANzksOOWYlv0oiIiIhS\nkfgmzY6bz1FiCxcuNF0CWcCcZGBOMjAnOeyYlfgmTfqFDzNJKBQyXQJZwJxkYE4yMCc57JiV+CZt\ncHDQdAlk0eHDh02XQBYwp/+/vXsPjiur7wT+/fW7W62XH5LGksayPbZnbM8IZKWMwTXjJCQQ2CWb\nbIVkQ0gCS8hWNoRi86Ly3q0iBcmQUIRNqhIqGbJhlyWbhSI8Ckgo26uN8EYWGGwntie2GdsztsEv\nqaVWqx9n/+jbUnerH1djuc/5dX8/VSqpb7eufq2vWvrp3nPP0YE56cCc9HAxK/VNGhEREVE7Ut+k\nRSIR2yWQT8PDw7ZLIB+Ykw7MSQfmpIeLWalv0sLhsO0SyKeRkRHbJZAPzEkH5qQDc9LDxazUN2lc\nYF0PFxevpbWYkw7MSQfmpIeLWalv0oiIiIjakfomLRgM2i6BfEomk7ZLIB+Ykw7MSQfmpIeLWalf\nYH1yctLMzMzYLoOIiIioqY5aYJ1j0vSYnp62XQL5wJx0YE46MCc9XMxKfZNWKBRsl0A+ZTIZ2yWQ\nD8xJB+akA3PSw8Ws1DdpRERERO1I/Zi0gwcPmlOnTtkug3zI5XIIhUK2y6AmmJMOzEkH5qRHq7Lq\nqDFpLh6epNouXLhguwTygTnpwJx0YE56uJiV+iYtm83aLoF8unXrlu0SyAfmpANz0oE56eFiVuqb\nNCIiIqJ2pL5Ji8fjtksgnw4cOGC7BPKBOenAnHRgTnq4mJX6Jk37hQ+dhOMHdWBOOjAnHZiTHi5m\npb5JW1pasl0C+XTx4kXbJZAPzEkH5qQDc9LDxazUN2lERERE7Uh9kxaJRGyXQD6Njo7aLoF8YE46\nMCcdmJMeLmalvkkLh8O2SyCfBgcHbZdAPjAnHZiTDsxJDxezUj8NMhdY12NmZgZHjx61XQY1wZx0\nYE46MCe7CgWDzEIWSwtZLKWySKe8j73b5e/RP4cf/vffbbvkCuqbNCIiImp/+WxhpcFKp8qarIUa\nH3u3M4u5uvsLhASxrjBiXWHEk2Enzy2qb9KCwaDtEsinnp4e2yWQD8xJB+akA3NayxiDbCZfbKIW\nckinlr3mKoel1DKWFnI1G65sJl93n6FoELGuEOLJCGJdIfRsjhUbsKT31lX23vs4HA1CRFb2MTs7\n24qnvy7qF1ifnJw0MzMztssgIiLqOKZgkEnnGh7NWntqMYd8rlB3n9FECFHv6FZ5U1XzfVcYsWQI\nobCeAzbrWWBd/ZG0VCpluwTyaWpqCkeOHLFdBjXBnHRgTjpoyqmQL6wexfLTcC0UGy5TqH2wRwKC\nWFdopanq2RLHwPaexg1XVwiBoJ3zji5mpb5J034ksJPkcvXHBpA7mJMOzEkHWznlsvni6cOFbOUp\nxNTy6vaF1YH0mSbjt4KhQLHhSkYQS4awaVtXwyNc8WQYkVgIEpC6+3SNi68p9U0aERFRu1oZv5Va\nexQrncoik6pstkpHt3INxm+Fo8GK8Vq9W+NrTh/GuyKIJcOIeuO8QpFAxfgtag39Y9LGes3Mb7t1\neJJqMzAQ8EXuOuakA3PSoTwnY4BMPoalXAxL2TiWcnEs5WJI51Y/zmTj3u3YyraCqX88JRpMIxZa\nQiycRizkfRxa/Ti+ZvsSgoH6DVwnM0MHID/wgYf+dTpqTFqhUH/wIbllYWEBya6k7TKoCeakA3Oy\nK18IFBuubKmZKr5VNFjZOBaWw8gWksUGLBeDqTPPg6BQbKLCxUaqN3YPg6EbiIfSiNZpuKKhJQRE\n94EWl9y+fRtbbBdRRX2TthDfBrztc7bLIB9mjh3jpI4KMCcdmNPGyS3nK08ZpopjtNZMfFp2//JS\n/aNRwXBg5XTi0nIKQyMDxSsV61yZGEtGEIkFeTrRsjPHjuGo7SKqqG/SiIiIAG/81tLahqvyasSq\n6SBSWeSy9c/IhGPBlYHwsa4wegcSDRoub/6tyOp0EMeOHcPRowda8fSpDalv0hKJhO0SyKfx8XHb\nJZAPzEmHds+pUDBYXixNdJprOhVE2jv6VcjXOf0nxfm3SpOdJvui2DKcbDjZaawrjGDowaaDaPec\n2omLWalv0vJ5DoDUYn5+Hv39/bbLoCaYkw6acsrnCrXn3qr13puBPrOYA+r0W4GAIJpcPbrVN5DA\n0M61pxBL827FkxFEEiEELEwHoSmnTudiVuqbtEwmY7sE8unSpUt49NFHbZdBTTAnHWzllF3ON5xN\nvnREq/wIV7bB+K1QOFBxNGtLf6zmKcTyU45hReO3+HrSw8Ws1DdpRES0fsYYLC/lKyc3rTq1uGbg\n/EIW+QbjtyKxYMWpw76hRNlM8rUbrlBEz3I+RK2mvkmLRqO2SyCfxsbGbJdAPjAnHcpzKhQMMouV\nY7bKZ5JPpypPJy6llpFZyKFQbzkfAaJlzVX3phi2PtpdcfqwdFqxuMZiBNGuEIKWlvNxGV9PeriY\nlfomLRjkf2FabNq0yXYJ5ANzsiufLaw5elXriNbC/SVMpV8qNmLpBuO3glJx+nDTUALRZO/K7Xj1\noPlkGNG4ruV8XMbXkx4uZqW+SVtcXLRdAvk0OzvLeZ0UYE4bwxiD3HKhOAh+IVc8fbhQuW5i9VQQ\nSwtZZBss5xOKBFaaqfTyArZtH0CsK1wxiL664QpH9Yzfakd8PenhYlbqmzQioofNFAwy6TrNVa2r\nFlPF04r5XP3xW9FEaOWUYqIngk2PdNW8MjFWdmoxFOb8W0SdRH2TFgqpfwodw7VLm6m2ds+pkC+s\nDo6vczRr7TxcOZgG47fKTyf2bIljYHvPmoHylfNwhRB4wPFb7Z5Tu2BOeriYlf4F1icnzczMjO0y\niMiCXDbf9PRh9WSnmcVc3f0FQoJ4reaqelvZfRy/RUTr0VELrM/Pz9sugXw6fvw4nnnmGdtlUBM2\ncjLGIJvJ15/stGpm+dLRrVyD8VvhaLCsoQqhZ0u8arxWyBs4X7wyMdala/wWX086MCc9XMxKfZNG\nemg/atspHjSnlfFb9SY7XcgiU+OqxUKu/teNJkIrDVZXXxSbh5NrjmjFq45+BcPtPR0EX086MCc9\nXMyKTRq1jJYjFJ2uPKd8vrByZWK9hmspVTYXlzcvV73fdRKQ4mB4r8Hq3RrH4I6ehg1XNPHg47fa\nEV9POjAnPVzMimPSiDpEcfxWeaOV82aYz2IplaucHsKbeX45XX/8VjAUqDp1GFk5tVhaxLo00Wnp\n1GIkHnLyFyERUat01Ji0dDptuwTy6fTp0xgfH7ddhnrGGGSX8hVHtmpNdlr9PrdcfzqIcCy4chQr\na5YwuGPTmuV7qgfPhyIBNlwW8fWkA3PSw8Ws1DdpuVz9//TJLXfv3rVdgnNMwSCzmKscFO+j4Srk\n651PLBu/1RVGsi+KLcNJRBs1XInK8VvF+bf2t+g7QC8XX086MCc9XMxKfZNG5Ip8vrDSRK1ZL7Fi\n3cTVbZnF+uO3AgFZaa5iXSH0DSQQ2xHyjmStnkKMeacWY8kwookwApwOgoioLahv0hKJhO0SyKeJ\niQnbJfiWXa4ev9Vgdnnv/fJS/ekgguEA4smwN0YrjC39VVcn1ngfidmZDkJTTp2MOenAnPRwMSv1\nTVo+X/8PI7nlzp076OnpaenXNMZgeal5w1V+ZeJSKotctv74rUgsWNFM9Q0m1jZaVacVw5Fg3f25\nxkZOtH7MSQfmpIeLWalv0jKZjO0SyKcrV65gbGzsZX9+oWCQWax9ZeLSwvLK9rR3ZeKSNx9Xoc5y\nPhAgllhtqLo3xbB1NLl6+tBrsEpHwFbm3wq193QQD5oTtQZz0oE56eFiVuqbNNIpnyvUPYWYTtWe\n7DSzmAPqjd8KSsXRrP6hqqNbZQ1X6XYkEeL4LSIicpb6Ji0ajdouoeOtjN+q03CVJju9fyeMv/zy\nP2BpIYtsg/FboUigosHq3hxr2nCFLY3fakc7d+60XQL5wJx0YE56uJiV+iYtGNQz1sd1xhgsp3Mr\npxDTqeXiGC3v1GHtqxWzyDcavxUPrZw6TPRE0d0fr5gKIlqj4QopGr/Vjrq7u22XQD4wJx2Ykx4u\nZqW+SVtcXLRdgpMKBeM1WP4nO80s5OqO3xJBxbis7s0xbN3eXXvuLe99tCuEYLB6/i1fkyyTRadP\nn8bRo0dtl0FNMCcdmJMeLmalvknrBPlsofZkp+WNV+l2qeFarD/JbyAkFWskbnqkC9FkGPEapxRX\nGq54CMLxW0RERC2jvkkLhfQ8BWMMspl8jbm2SlcqVq6bWFrAOpdpMH4rGqxYK7GnfPxW9dxbpekg\nonbGb23evLnlX5PWjznpwJx0YE56uJgVF1h/mUzBILMyfqv20azqU4rphSwKufrf72gitDLZaa2j\nWWsbrhBCYT3jtwqFAgKB9p6+oh0wJx2Ykw7MSY9WZaVigXURiQMYNcZceJD9zM/PP3AthXyh7CiW\nj4bL+7hefysBqZhnq2dLHAPbe+o2XPFkGNFECIFge7+QT5w44dz5flqLOenAnHRgTnq4mFXLmzQR\n6QHwlwC+B8AnAbyj6v4DAD4OoA/AZwC82xhT//LBKrls3pvcNLv2FGKq7CrF0txbTcZvBUMBb13E\n4lqJm7Z1rZnstLrhisQ4fouIiIgejI0jaQUAfwTgswBeVeP+PwbwXgBfAvAVAG8C8Ol6O1ueB/7n\n+/7fyuLVjcZvhaPBivFavVvjFacP41VXJsaTEYQiAc6/tUE0jR/sZMxJB+akA3PSw8WsWl6RMSYF\n4O9F5Ker7xORrQB2GGO+4N3+OIDXo6pJE5F3AngnAIwO7MJSPoVgD/DoY33o7ovj1p0bCEWB/q09\neHz/bnz9zCkEI0AkGsSRI6/G7Ows5ubuAQAmJidx8+ZNXL36PLAA7N62GxItYPabpwAAAwMD2LNn\nD6ampgAUJ889fPgwZmZmkEqlAACHDh3CtWvXcP36dQDA3r17EQwGce7cOQDA0NAQduzYgenpaQBA\nPB7HoUOHcPLkSaTTaQDA4cOHcfnyZdy4cQMAsG/fPuTzeZw/fx4AMDw8jJGREZw8eRIAkEwmMTk5\nienp6ZWlsY4cOYILFy7g1q1bAIADBw4gk8ng4sWLAIDR0VEMDg6iNIavp6cHExMTmJqaQi5XPJr4\n9NNP4+zZs7h9+zYAYHx8HPPz87h06RIAYGxsDJs2bcLs7CwAoL+/H+Pj4zh+/DiMMRARPPPMMzh9\n+jTu3r1b/B5PTODOnTvI5XI4duwYdu7cie7ubpw+fRpAcbDm/v37ceLECQDFF8qRI0e8nOYAAJMr\nOV0FAOzevRvRaBRnzpxhTsyJOTEn5sScHiinK1euAABeeOGFh57Teli7cMBr0o4YY95Rtu2VAD5i\njHmNd/sNAH7WGPOD9fazb98+U/phI7fNzs5iYmLCdhnUBHPSgTnpwJz0aFVW67lwwLWR6hEUT4eW\nFADUP38JIJ9veDc5pPRfB7mNOenAnHRgTnq4mJVrTdpLAIbLbo8AuGqpFiIiIiJrnGrSjDEvAFgQ\nkaMiEgTwVgB/3ehzurq6WlIbPbjJSS4JpQFz0oE56cCc9HAxq5Y3aSLSLSLPA/gAgB8RkedF5IdE\n5Je8h/wUild/XgFwwhjTcKRdNpt9qPXSxrl586btEsgH5qQDc9KBOenhYlYtb9KMMfPGmMeMMYPG\nmF7v408ZY5717p81xjxpjBk1xvxms/0tLy8//KJpQ5SufCG3MScdmJMOzEkPF7Ny6nQnERERERWp\nb9JisZjtEsin3bt32y6BfGBOOjAnHZiTHi5mpb5J42oAekSjUdslkA/MSQfmpANz0sPFrNQ3aaUZ\nkcl9pdmXyW3MSQfmpANz0sPFrNQ3aURERETtSH2TFg6HbZdAPg0MDNgugXxgTjowJx2Ykx4uZmVt\n7c6NcvDgQXPq1CnbZZAPuVwOoVDIdhnUBHPSgTnpwJz0aFVWmtfuXLdUKmW7BPJpaqrhvMTkCOak\nA3PSgTnp4WJW6ps0IiIionakvkkLBNQ/hY7h4uXNtBZz0oE56cCc9HAxK/Vj0iYnJ83MzIztMoiI\niIia6qgxaYuLi7ZLIJ/YTOvAnHRgTjowJz1czEp9k5bP522XQD7xIg8dmJMOzEkH5qSHi1mpb9KI\niIiI2pH6MWkTExNmdnbWdhnkQzqdRjwet10GNcGcdGBOOjAnPVqVVUeNSctms7ZLIJ+uXbtmuwTy\ngTnpwJx0YE56uJiV+iZteXnZdgnk0/Xr122XQD4wJx2Ykw7MSQ8Xs1LfpBERERG1I/VNWiwWs10C\n+bR3717bJZAPzEkH5qQDc9LDxazUN2kiYrsE8ikYDNougXxgTjowJx2Ykx4uZqW+SUun07ZLIJ/O\nnTtnuwTygTnpwJx0YE56uJiV+iaNiIiIqB2pb9LC4bDtEsinoaEh2yWQD8xJB+akA3PSw8Ws1Ddp\nLq5aT7Xt2LHDdgnkA3PSgTnpwJz0cDEr9U2ai2ttUW3T09O2SyAfmJMOzEkH5qSHi1mpb9KIiIiI\n2pH6Ji0QUP8UOgbXr9OBOenAnHRgTnq4mJX6BdYnJyfNzMyM7TKIiIiImuqoBdYXFhZsl0A+nTx5\n0nYJ5ANz0oE56cCc9HAxK/VNWqFQsF0C+cSJh3VgTjowJx2Ykx4uZqW+SSMiIiJqR+rHpB08eNCc\nOnXKdhnkQyaT4bx2CjAnHZiTDsxJj1Zl1VFj0jKZjO0SyKfLly/bLoF8YE46MCcdmJMeLmalvknL\nZrO2SyCfbty4YbsE8oE56cCcdGBOeriYlfomjYiIiKgdqW/SXJx8jmrbt2+f7RLIB+akA3PSgTnp\n4WJW6ps07Rc+dJJ8Pm+7BPKBOenAnHRgTnq4mJX6Jm1pacl2CeTT+fPnbZdAPjAnHZiTDsxJDxez\nUt+kEREREbUj9U1aJBKxXQL5NDw8bLsE8oE56cCcdGBOeriYlfomLRwO2y6BfBoZGbFdAvnAnHRg\nTjowJz1czEp9k8YF1vVwcfFaWos56cCcdGBOeriYlfomjYiIiKgdqW/SgsGg7RLIp2QyabsE8oE5\n6cCcdGBOeriYlfoF1icnJ83MzIztMoiIiIia6qgF1jkmTY/p6WnbJZAPzEkH5qQDc9LDxazUN2mF\nQsF2CeRTJpOxXQL5wJx0YE46MCc9XMxKfZNGRERE1I7Uj0k7ePCgOXXqlO0yyIdcLodQKGS7DGqC\nOenAnHRgTnq0KquOGpPm4uFJqu3ChQu2SyAfmJMOzEkH5qSHi1mpb9Ky2aztEsinW7du2S6BfGBO\nOjAnHZiTHi5mpb5JIyIiImpH6pu0eDxuuwTy6cCBA7ZLIB+Ykw7MSQfmpIeLWalv0rRf+NBJOH5Q\nB+akA3PSgTnp4WJW6pu0paUl2yWQTxcvXrRdAvnAnHRgTjowJz1czEp9k0ZERETUjtQ3aZFIxHYJ\n5NPo6KjtEsgH5qQDc9KBOenhYlbqm7RwOGy7BPJpcHDQdgnkA3PSgTnpwJz0cDEr9U0aF1jXY2Zm\nxnYJ5ANz0oE56cCc9HAxK/VNGhEREVE7Ut+kBYNB2yWQTz09PbZLIB+Ykw7MSQfmpIeLWalfYH1y\nctK4eIiSiIiIqFpHLbCeSqVsl0A+TU1N2S6BfGBOOjAnHZiTHi5mpb5J034ksJPkcjnbJZAPzEkH\n5qQDc9LDxazUN2lERERE7Yhj0qhlCoUCAgH+X+A65qQDc9KBOenRqqw6akxaOp22XQL5dPbsWdsl\nkA/MSQfmpANz0sPFrNQ3aS6eQ6babt++bbsE8oE56cCcdGBOeriYlfomjYiIiKgdqW/SEomE7RLI\np/HxcdslkA/MSQfmpANz0sPFrNQ3afl83nYJ5NP8/LztEsgH5qQDc9KBOenhYlZWmjQRebOIXBaR\n50Xk7VX3PSci1737nheRRxvtK5PJPNxiacNcunTJdgnkA3PSgTnpwJz0cDGrUKu/oIh0A/gggFcB\nyAP4uoj8rTHmqoA+WQAAH8tJREFU22UPe4sx5lirayMiIiJyhY0jaa8DcNwYc90YcwPAVwB878vd\nWTQa3bDC6OEaGxuzXQL5wJx0YE46MCc9XMyq5UfSAIwC+FbZ7WsAHim7nQXwMRFJAfhzY8wHq3cg\nIu8E8E4A2LZtG44dOwYA2LlzJ7q7u3H69GkAwObNm7F//36cOHECABAKhXDkyBHMzs5ibm4OADA5\nOYmbN2/i6tWrAIDdu3cjGo3izJkzAICBgQHs2bNnZU2vaDSKw4cPY2ZmZmXd0EOHDuHatWu4fv06\nAGDv3r0IBoM4d+4cAGBoaAg7duzA9PQ0ACAej+PQoUM4efLkyjxvhw8fxuXLl3Hjxg0AwL59+5DP\n53H+/HkAwPDwMEZGRnDy5EkAQDKZxOTkJKanp1dO+R45cgQXLlzArVu3AAAHDhxAJpPBxYsXi9/4\n0VEMDg6iNPlvT08PJiYmMDU1tTKVydNPP42zZ8+uXIo8Pj6O+fn5lcPAY2Nj2LRpE2ZnZwEA/f39\nGB8fx/Hjx2GMgYjgmWeewenTp3H37l0AwMTEBO7cuYNLly7hypUrzIk5MSfmxJyYk1M5XblyZWUy\n24ed03q0fMUBEflVAEljzG96t98P4EVjzIerHjcK4MsAft4Y83f19rd3715T+kEhtx07dgxHjx61\nXQY1wZx0YE46MCc9WpWV6ysOvARguOz2CICr1Q8yxlwF8FkAB1pUFxEREZEzbDRpXwTwOhEZEJEh\nAK8G8KXSnSLymPd+M4DXA/jHRjsLhWycsaWXo7+/33YJ5ANz0oE56cCc9HAxKysLrIvITwP4Te/m\nL3nvdxljnhWRzwPYByAD4I+MMR9ptC8usE5ERERauH66E8aY54wxu7y3T3lvz3r3vcEYM2aM2dus\nQQPcnHyOajt+/LjtEsgH5qQDc9KBOenhYlbqVxwgPWwctaX1Y046MCcdmJMeLmbFJo1aRkRsl0A+\nMCcdmJMOzEkPF7OyMiZtI3FMGhEREWnh/Ji0jVSabI/cV5ockNzGnHRgTjowJz1czEp9k1aaiZjc\nV5rhmdzGnHRgTjowJz1czEp9k0ZERETUjtQ3aYlEwnYJ5NPExITtEsgH5qQDc9KBOenhYlbqm7R8\nPm+7BPLpzp07tksgH5iTDsxJB+akh4tZqW/SMpmM7RLIpytXrtgugXxgTjowJx2Ykx4uZqW+SSMi\nIiJqR+qbtGg0arsE8mnnzp22SyAfmJMOzEkH5qSHi1mpb9KCwaDtEsin7u5u2yWQD8xJB+akA3PS\nw8Ws1Ddpi4uLtksgn1ycKJDWYk46MCcdmJMeLmalvkkjIiIiakfqm7RQKGS7BPJp8+bNtksgH5iT\nDsxJB+akh4tZcYF1aplCoYBAQP3/BW2POenAnHRgTnq0KquOWmB9fn7edgnk04kTJ2yXQD4wJx2Y\nkw7MSQ8Xs1LfpBERERG1I/WnO7cPDpjf+7m32y6DfLh//z56e3ttl0FNMCcdmJMOzEmPXDiGt/za\n7zz0r9NRpztDnCdNDf6i0oE56cCcdGBOemzbts12CWuovzQy2tePH/3t99sug3yYnZ3FxMSE7TKo\nCeakA3PSgTnpMTs7a7uENdQfScvn87ZLIJ/m5uZsl0A+MCcdmJMOzEkPF7NS36QRERERtSP1Fw5M\nTEwYFw9R0lqpVArJZNJ2GdQEc9KBOenAnPRoVVYddeFANpu1XQL5dPPmTdslkA/MSQfmpANz0sPF\nrNQ3acvLy7ZLIJ+uXr1quwTygTnpwJx0YE56uJiV+iaNiIiIqB2pb9JisZjtEsin3bt32y6BfGBO\nOjAnHZiTHi5mpb5JExHbJZBP0WjUdgnkA3PSgTnpwJz0cDEr9U1aOp22XQL5dObMGdslkA/MSQfm\npANz0sPFrNQ3aURERETtSH2TFg6HbZdAPg0MDNgugXxgTjowJx2Ykx4uZqV+MtuDBw+aU6dO2S6D\nfMjlcgiF1C8X2/aYkw7MSQfmpEerslrPZLbqf3JSqZTtEsinqakpHD161HYZ1ARz0oE56cCc7DPL\ny8jdu4f8vXvI3/Xe37uH/N27FR9f37EDr3rvr9out4L6Jo2IiIjanzEGJp1G/t495MobrCbNV2Fx\nse4+JZFAsK8Xob5+yMhwC5+NP+qbtEBA/bC6juHi5c20FnPSgTnpwJxqM8agMD+/pqmqbL7ur2m4\nTINVhgI9PQj29SHY34fgls2IPrYLwb7+4u2+vuLHpfv7im+BsnxuTE+34qmvi/oxaZOTk2ZmZsZ2\nGURERB3J5HLIz81VNlRlzVeu+kiX94Z8vvYOg0EEe3sR7O9faaaC/X0I9fWV3e6v/LinB6Jk7F9H\njUlbbHAYk9wyMzODyUlfP5dkEXPSgTnpoC2nwvKy11DdrWqsVm/n7t2tOM1YmJuruz+JRCqaquhj\nj1UcyQqVN1ve4wLJJMTCWTIXs1LfpOXrdeLkHF7koQNz0oE56WArJ2MMzOKidwqxznit6lON9+7B\nNDjwEUgkKo5gRUZG1xztqm6+JB5XszKQi68p9U0aERFROzOFQnH8Vvnpw0aD5Uvjt7LZ2jsUQaCn\nZ+X0YWjrVkT37FlzRKu6+QpEIq194qR/TNrExISZnZ21XQb5kE6nEY/HbZdBTTAnHZiTDtU5mVwO\n+fv3GwyWr9F83b8PFAq1v0Aw6DVUvXVOIfZXHOFaGb8VDLboO6BHq15THTUmLVvvPwVyzrVr17B7\n927bZVATzEkH5mRfIZOpOeVDefM1f/1FRLPZ1ekg5ufr7k+i0YojWNE9e1YarFCtwfJ9fcXxW0pO\nJ7rOxdeU+iZtucHluOSW69evO/cCoLWYkw7MaeMYY1BYWFw7WL7iCNfaKxVNOl13n4GuLgT7+7Ec\nDCIxOorI9u1eg9W79mhXqeHikVGrXHxNqW/SiIiISkyhgMLcXOUpxOrpHyoGy99F/t59oMH4rWDv\n6qnE8MAgYnsfbzhYPtjbC/HGbx07dgxPccUBepnUN2mxWMx2CeTT3r17bZdAPjAnHTohJ1M6TVh2\n9WGxwbpf/zTj3Fz98Vuh0Op8W719iIxtR7zvFQ0Hyz/o+K1OyKlduJiV+iaN5+L1CHKgqgrMSQdt\nORWWltY0VbmKo1trj3QVGkyJILFYWVPVi9i+JxpcneidTuzqavnfDG05dTIXs1LfpKUbjAkgt5w7\ndw4DAwO2y6AmmJMOtnIqjt9aaDhYvtayPmZpqe4+A8lk5fxbY2P1JzwtNVxKzqLw9aSHi1mpb9KI\niOjlMfm8t5zP2lnlywfL5++ujt3K37sH5HK1d1g+fqu/H+GhIcQef7ziiFewv391eZ/+/uL4rXC4\ntU+cSAn1TVqYL241hoaGbJdAPjAnHapzMsvLTU8f1hy/VW+uzHAYwb5er6HqR3THzvrjtryjXYGe\nHivL+biMryc9XMxKfZMWLVvBnty2Y8cO2yWQD8zJLmMMTDpdOWC+xpWKsTt3cPn+/ZXthYWFuvuU\neLysmepDeNsjqxOdVjRbqxOf2hi/1Y74etLDxazUN2kurrVFtU1PT+MoL0V3HnPaOMaY4nI+ddZJ\nrHeloslk6u4z0N2NYF8fFgMB9G1/FJFdO2svVK1w/FY74utJDxezUt+kERG1gsnni8v51DqFWH6l\nYvlpxvv364/fCgQqx28NDyO2f3/9ubdK8295Qzw4/xZR+1PfpAU4/kENrjOoQyfkVFheXm2mqmeV\nL2uycqWB8/fuo3D/ft39SThccfQqumvX2vFbfb0VDdeDjt/qhJzaAXPSw8Ws1C+wPjk5aWZmZmyX\nQUQWGGNgFhfXLNfTcLD8vXsoLC7W3ackEt6A+f6apw7XNl99CHQlOH6LiHzpqAXWFxoMliW3nDx5\nEocOHbJdBjVhKydTKKyO36p3+rDGaUZTbzkfAIGentVmausWRHc/VjE4vnqwfLCvDwElFyPx9aQD\nc9LDxazUN2mFest/kHM48bAOG5GTyeWK47fqTnJa46jX/fv1l/MJBovjt7wjWOHRUcSePFBzktOK\n8Vsh9b/i6uLrSQfmpIeLWbXvbzAi2hCFpaX6R7Iqmq/VpqwwP193fxKJVDRU0d276w+U95qvQDLJ\n+beIqOOoH5N28OBBc+rUKdtlkA+ZTIbz2lm0spxPxVGsu5Uf37uH7J07KNyfW50OosF/l4FEov5Y\nrYpTiqvNl8TjHL+1Afh60oE56dGqrDpqTFqmwXxC5JbLly/j8ccft11GWzCFAgpzczUnOa11xWLO\nO9KFeuO3RBD0xm8tx6JIPrINsb17mzZfgUiktU+cVvD1pANz0sPFrNQ3adkGg4bJLTdu3HDuBeAC\nk81WjN9qNMlpxXI+9cZvhUKr6yR6i1XHywfJ15phvqcHEgwCKM6/9QTn33IeX086MCc9XMxKfZNG\n5JKV8Vv1BszXuFKx0GDVDIlGK8dvPfF47bFb5fNvJZM8nUhE1AbUN2kuTj5Hte3bt892Cb5Vjt+q\ncSSrogFbPeJllpbq7jPQ1VXRTEXGxlaPePX3ewtZVzVcFn6+NeXUyZiTDsxJDxezUt+kab/woZPk\n83krX9fk88jPzTWeb6s0gP7+Pf/jt0rTQQwOIvb44zXHbK0c8erthSgZv2UrJ1of5qQDc9LDxazU\nN2lLDY5ckFvOnz+PRx555IH2YZaXVyc5bTpg3rs9NwfUa+a98Vuh/j4Ee0vjtxrNNF85fqsdbURO\n9PAxJx2Ykx4uZqW+SSOdjDEw6XSd+bbqzzJfaLDChMRiZQ1VL2Lbnmi6rE+gq4vjt4iIyEnqm7SI\nklNI7cwYs7qcT91B8/cx9OKLuPSHH1qdf6vB9CmB7u7VhmpTPyI7dzQfMB+LtfBZt6/h4WHbJZAP\nzEkH5qSHi1mpb9LC4bDtEtqKyeeL00HUWSex5nqK9+8DuVztHQYCxeV8+voQ6e1FeHgYsf3714zd\nqmi8enshzNWakZER2yWQD8xJB+akh4tZqW/SuMB6fYXl5frjtcqPdt1bPdpVaDB+S8LhiiNY0V27\naqyZ2FvRcAV6elaW8zl27BiOcv4t5508eZI5KcCcdGBOeriYlfomrROsjN+qdySrTgNWWFysu09J\nJFYmOw319SMyPFJ7keryhqsrwfFbRERELaK+SQsqu8puZfxW3UWqa1+taJaX6+4z4C3nE+zrQ3DL\nZkQf29VwsHywrw+BGuuTlU9nUvqw/JhavmBWtpiqxxW3mTXbyvcXjnUhvZyv+bjV/Zk12yoe2+Tr\nNdpPrVpR83P9fY3yr1Pv4tHV7+Pa722zeisf2+zzm9S8jpxuZqP45rX7NWuu+dx91lvrcQ+SU+W+\n119r05+lFuXUrOaKkss2XbodxN2vXav8/GY/pxU781vH2pprfp0m35vmWa99XEW5G1Tv6uMe8DVV\no7hadbz0EvCPX/zndX2d8gc0+33j9/VQWa6/112zr1Pzdb6un/G1j6v9O3n9Pzu+f9bLHvh4MoSj\ncIv6BdaTI3vN+M//yQP90JlaaaLeD9XqizFQyCO5vIiupQV0Ly8guZRCd2ax+HFmAd0Zb3tmEd2Z\nFLqXF5FcXkTQ1F7OJw9BKtqF+UgC85EuzJV/HEl4t7u828X75iJxFALBBs+t2R8VIiJ6UKWTDFKx\nbfWWVD2uuG3tJ1V+ftXj1vF16u9TatThr140raN+vfW+Ts3H1fge+a236fNuUO9bXvUofvLw2Jra\nNlpHLbAeDRgc3rUZwDp+uGv80AVzy4guphBdnEdscR7RlbcUogtziC2mEKnaHknXHw+XD4aQ6erB\nciKJ5d5uZLoG8Z1EN17sSmI50Y1MVw+yiW4sd3VjOdmN5UQ3srFExfxb5S+SXhTfmr9Yy59Z/R/u\n8jte7uevfj+bvOC8z3rhhW9h+/btFfup+QsL1RlVfp3aOdd4XK26ff7SrP0LoXatNX7PNv/l3ORr\nlmv0vNdTc/NfsMVb58//Mx7f+3jdmv0+95fzxwY+H1fx/W34Olj/H7f1/UyufezL+WPTrObK+oof\nfe1rX8PEK1+55rHrqvlBfges67n5+5lYyf8B9/OysvL7ddY55GN6ehqHDx9e1+eQHdPT0wDGbJdR\nwUqTJiJvBvABAHkAv2uM+fOy+w4A+DiAPgCfAfBuY+ocegKwJS549kfGV24Xl/NZrD+xadkM86uT\not6HaTB+K5BIrJ4yfHQQwb69dcZv9a0s7SMJjt+qduzYVRx9ZpftMqiJ8K1/wtF9g7bLoCa+Fc5h\nbEuX7TKoiUyDqYbILS5m1fImTUS6AXwQwKtQbNK+LiJ/a4z5tveQPwbwXgBfAvAVAG8C8Ol6+wt+\n+zv41lt/suxKxXv1l/MBEOjtLV6B2NeP8NYBxHbvaThYPtjfhwDnYiMiIqIWs3Ek7XUAjhtjrgOA\niHwFwPcC+ISIbAWwwxjzBe++jwN4PaqaNBF5J4B3AsDjiS7cu3sXha4uJB/bha4tW3BjYQGFZBLJ\noUcw9tST+Nrzz6OQTCLY04MjTz+N2dlZzM3NAQAmJydx8+ZNXL16FQCwe/duRKNRnDlzBnjpRQwM\nDGDPnj2YmpoCAESjURw+fBgzMzNIpVIAgEOHDuHatWu4fv06AGDv3r0IBoM4d+4cAGBoaAg7duzw\nDqUWF4U/dOgQTp48iXQ6DQA4fPgwLl++jBs3bgAoLvSaz+dx/vx5AMVJ9kZGRnDy5EkAQDKZxOTk\nJKanp1e6/yNHjuDChQu4desWAODAgQPIZDK4ePEiAGB0dBSDg4OYmZkBAPT09GBiYgJTU1PIefOc\nPf300zh79ixu374NABgfH8f8/DwuXboEABgbG8OmTZswOzsLAOjv78f4+DiOHz8OYwxEBM888wxO\nnz6Nu3fvAgAmJiZw584dAMVpOHbu3Inu7m6cPn0aALB582bs378fJ06cAACEQiEcOXLEf04Ac2JO\nzIk5MSfm9LJzunLlCgDghRdeeOg5rUfLLxwQkfcA2GKM+XXv9u8BeMkY84ci8koAHzHGvMa77w0A\nftYY84P19nfgwAFT+kaQ286dO4d9+/bZLoOaYE46MCcdmJMercpqPRcOBB52MTVEAJSPMSugeNqz\n2X01ZRuc2iS3lP6DIrcxJx2Ykw7MSQ8Xs7LRpL0EoHyBrBEAV33cR0RERNQxbDRpXwTwOhEZEJEh\nAK9G8SIBGGNeALAgIkdFJAjgrQD+utHO4vH4w66XNsiBAwdsl0A+MCcdmJMOzEkPF7Nq+YUDxpib\nIvLrAKa9Tb8I4PtFZJcx5lkAPwXgYyhOwfGcMabhSDvtk/F2Ehcvb6a1mJMOzEkH5qSHi1lZmSfN\nGPMcgOfq3DcL4Em/+1paWtqYouihu3jxIoaHh5s/kKxiTjowJx2Ykx4uZmXjdCcRERERNaG+SYtw\nolk1RkdHbZdAPjAnHZiTDsxJDxezUt+khcNh2yWQT4ODXGpIA+akA3PSgTnp4WJW6pu0hYX6i5yT\nW0ozSZPbmJMOzEkH5qSHi1mpb9KIiIiI2pH6Ji0YDNougXzq6emxXQL5wJx0YE46MCc9XMyq5Wt3\nbrTJyUnj4iFKIiIiomqur925oVKplO0SyKepqYbzEpMjmJMOzEkH5qSHi1mpb9K0HwnsJLlcznYJ\n5ANz0oE56cCc9HAxK/VNGhEREVE74pg0aplCoYBAgP8XuI456cCcdGBOerQqq44ak5ZOp22XQD6d\nPXvWdgnkA3PSgTnpwJz0cDEr9U2ai+eQqbbbt2/bLoF8YE46MCcdmJMeLmalvkkjIiIiakfqm7RE\nImG7BPJpfHzcdgnkA3PSgTnpwJz0cDEr9U1aPp+3XQL5ND8/b7sE8oE56cCcdGBOeriYlfomLZPJ\n2C6BfLp06ZLtEsgH5qQDc9KBOenhYlbqmzQiIiKidqR+njQRmQdw3nYd5MsWAN+xXQQ1xZx0YE46\nMCc9WpXVdmPMVj8PDD3sSlrgvN9J4cguEZlhVu5jTjowJx2Ykx4uZsXTnUREREQOYpNGRERE5KB2\naNL+1HYB5Buz0oE56cCcdGBOejiXlfoLB4iIiIjaUTscSSMiIiJqO2zSiIiIiBzEJo2IiIjajojE\nRWSP7ToehOomTUTeLCKXReR5EXm77Xo6jYjERORPReS8iHxLRN7jbX+3iLzgbf+Bsse/X0Suicg3\nReSgty0kIs+JyHUR+aqI7LD1fNqdiERE5JyIfNS7zZwcJCK9IvIJ73v9L15uzMoxIvKfROSi9zfo\nP3rbmJMDRKRHRD4N4CaAXynb/sD5iEi3iHzWe/yXRGTzQ30yxhiVbwC6AVwFMAxgCMANAFtt19VJ\nbwA2A/i3AATFmZpvAngGwAUvn30AXgQQBvA9AKZQnED5+wB83dvH2wF8wtvHzwD4tO3n1a5vAH4H\nwOcBfBTALubk5huAvwTwG973Osas3HsDMAbgCoAu7/fgfQD7mZMbbwCSAL4XwDsAfNTbtiGvIwD/\nBcAHvI/fB+BDD/O5aD6S9joAx40x140xNwB8BcVQqEWMMbeNMX9jir6DYtP8NIBPGmPmjTHnUPxF\ndhDADwN4zhiTM8Z8GcBWERnytn/UFH/iPw7gtVaeTJsTkScAfBeAT3qbfgjMyTne9/rVAH7Xe10t\ngVm5KOu9L6D4xz0F4A1gTk4wxqSMMX8PIFe2eaNeRz8M4M+8jz8G4PUP87lobtJGAXyr7PY1AI9Y\nqqXjicgBFP/r34LauVTndb16uzFmEcCiiPS3ouZOISIC4MMA3l22ud7rhznZtR/AZQB/452SeRbM\nyjnGmOsoHpn+KoC/A/DvAIyAOblso15HIwBeqNrHQ6O5SYug+F9MSQFA3lItHU1EtgD4bwDehvq5\nrHc7bZz/AOCYMeb5sm3MyU0DKJ6KeReACQCvAfAmMCuniEgPgB9H8R+fPwDwS+BrynUblU/59oee\nmeYm7SUUx6OVjKB4uo1ayPvP4m8B/Jox5h9RP5fq7dtQ/C9kZbuIxAGEjDFzLSi9k7wVwI+JyNdR\nHE/xQyiO4WRO7rkF4JQx5poxZgHAlwE8B2blmp8A8A1jzDFjzF942/iacttG/W264T2mfB8PjeYm\n7YsAXiciA2XjOL5kuaaO4v03+RkA7zPGfMHb/DkUG4KENw5qE4Cve9t/SkSCIvJ9AC4YY+5429/m\nfe5PAPh0S59EBzDGvNoY86Qx5hUAfgvApwB8FszJRV8FsE9EtolIFMVxMCkwK9csAXiFiIRFpBvA\nHhRPezInd23U36bPoXhRAbz7//phFh16mDt/mIwxN0Xk1wFMe5t+0fvPk1rnF1A8JfMhEfmQt+37\nAfwVgLMo/iJ7hzHGiMinULzy8xKA2yieKgCA/wrgL0Tkqnffj7aw/o5ljDklIszJMcaYBRF5F4pH\n0KIoDmj+oNewMSt3/BWKVwVeApAG8DFjzP/la8oNXuP8NRSv5IyJyFEUr9DciHx+G8D/EJFrAE6V\nPf7hPBfvMlIiIiIicojm051EREREbYtNGhEREZGD2KQREREROYhNGhEREZGD2KQREREROYhNGhER\nEZGD2KQREREROYhNGhEREZGD2KQRUUcQkYCI/LyIfE1E0iIyJyJnReTDIiJVj32ziNyo3k5E1Epq\nl4UiIlqnT6C4bNkHUVwjM4nimr/fbdYuvfJGAJ+vsZ2IqGW4LBQRtT0R+QEAnwfwBmPMF6ruk/Jm\nTEQCAF4C8HPGmL9pbaVERKt4upOIVBORLSJiROS1Vds/JCJf9W4+473/SvXn1zha9l0A+lFc5Ly0\nr6CIvEdEviEiSyLykoh8XIoCIrIgIu8WkT8QkVsicldEftn73LeKyDkRSYnI/xaR+IY9eSJqa2zS\niEi7ce/96artTwH4pvfxgvf+90Vke5P9vRHA/zHGzAErR9b+F4DfAvBxAP8KwK8BCHsN3k4ACQDv\nAZAB8OMAPgfg90TkIwB+DMAvA3gvgH8D4G0v4zkSUQfimDQi0u4VAF4yxny7avs4gE95H/8ZgB8B\n8C4A7xKRswD+O4APG2NSVZ/3RhSbsZL3APg+AN9ljPmnsu1/4b1/ynv/B8aYDwOAiFwE8BYATwB4\nbelonYi8E8Del/Usiajj8EgaEWk3jqqjaCIyAmATgG8AgDHmBoBXAngdgD8B0AfgfQD+QUQiZZ/3\niPe4z3m3AwB+BcBHqhq0ck8CuOftt6TLe//+qtOpXQDurP8pElEnYpNGRNqtadKwegr0G6UNxpi8\nMeZLxpifA/AoikfCngRwuOzz3gDgkjHmvHf7KQADWD0iV8uTAKaMMdmybU8ByAE4UdogIgkAYwDO\n+HtaRNTp2KQRkVreUbAnsLbxeQ2Aa8aYu7U+zxhTAPAl72as7K43wjuK5nnEe/9SgzKeAvD1qm3j\nAP7ZGJMp2/Ykir9zvwEiIh/YpBGRZvsAhAEUShtEJInieLBvercH63zumwAsAjjpPS4C4LWobNJu\neO+fqLUD70rNXah90UKtbQsA/qXREyIiKuGFA0Sk2TiAPIDfEJE8ir/TfgHAEIDLIjIO4MMiMg/g\nkwCuoHj68i0AfhDAzxhj7nn7ehrFf1yPl+3/mwDOAvgTEfktAC+i2BiOGmN+FcB+73NqNWQfrrHt\nrHcUj4ioKTZpRKTZK1A81fkpAB8FMAfgP6M4zuxNKDZrHwPwZgC/i2KDlgIwDeB7jDHHyvb1RgB/\nV36K0hiTE5F/DeBZAH+I4lQbFwG833vIkygejVs5OiYi/QBGsPa05lM1thER1cUVB4hILRH5CoAX\njDE/vQH7ugDg940xf/bAhRERbQAeSSMizcYBfGYjdmSM2bMR+yEi2ii8cICIVCqbC636ykoiorbA\n051EREREDuKRNCIiIiIHsUkjIiIichCbNCIiIiIHsUkjIiIichCbNCIiIiIHsUkjIiIichCbNCIi\nIiIH/X/nGk1HkHRv5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a9c1588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c, d, l, r1= best[C], best[D], best[L], best[R1]\n",
    "errors(l, d, c, r1, maxF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$0.000276645147855$$"
      ],
      "text/plain": [
       "0.000276645147855"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l / (np.pi * (d / 2)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANMAAAASCAYAAADBs+vIAAAABHNCSVQICAgIfAhkiAAABppJREFU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\n",
      "text/latex": [
       "$$6899.860323601468$$"
      ],
      "text/plain": [
       "6899.860323601468"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  }
 ],
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